You are NOT the failure here. What I think you did was lose a little of yourself to these people who were undeserving at the time, hey...I believe that if we are all honest we'll own to that happening at first. After a while, though, I found ME again and things changed.
Your DH has a drinking problem you said, it's HIS problem that he goes into denial and blames you for whatever he can. Where your problem lies is that you accept the blame, by resigning yourself to the situation at home and feel bad...STOP IT!! I am sorry if that sounds harsh but I tell it like it is.
Can you do stuff just for you? I know taking care of two infants is hard work, I raised three kids on my own before I met DH here.
The reality of the situation, in my opinion, is that your DH is refusing to speak because he knows he behaved like a total ass. I would ignore him, and his sulking, just the same way as I would ignore a petulant child. At least SD 20 knows the reality of the situation, remember they have all had more previous experience of your DH than you have and they are not blaming you in any way! Please vent though, it's more aggravating to have to keep it all to yourself...believe me! I have found this site to be an enormous help with all the different perspectives here.
One day Your DH will wake up and decide to quit drinking, nothing or no one can make him do it.

Then let him leave...he'll get drunk...lament to someone...they'll humor him because he's drunk. I bet he comes back when he sobers up and he will feel guilty as hell because that's how drunks are. Just say something along the lines of 'Oh, you're back! I am just on my way out so I'll see you later.' Or just go about your business of the day and disregard him, without being mean or judgemental until at least a day later, it takes time for the effects of the alcohol to leave their system. It's not a good thing to try and rationalize with someone who is under the influence, they believe their own fiction, for one thing, and you will not be able to shift their thinking no matter how much logic you apply to yours.

Where ever you live, it's important for you to have a friend that lives close to you. Not saying that he will, but if he gets physical with you, you need to have a plan ready. If you have any neighbors, go introduce yourself to them and let them know where you live. I'm glad you haven't let him keep you down. The insecurities he has cannot be fixed by you. If I had to guess, I'd say he probably never got his dad's affirmation that he was proud of him. Guessing again, he probably has a strained relationship with his dad. Hang in there!

Do you know your immediate neighbors? I'd get to sitting outside, it's summer time and the kids can be supervised playing out,or you could be gardening with their 'help' and get to know who is passing by and getting aquainted with them. Put the kids in their stroller and go to the local park, see how many people are there...anything that is going to amuse and entertain the kids so they are not picking up on how stressful this whole mess is. Meeting new people can be daunting if you've been isolated, raising small kids is not the easiest iether. I used to pack a picnic and walk to the park with mine when they were small. Once you meet folks you might even find a babysitting circle? It's a small world in reality and there are people out there who might just benefit from what you are learning to deal with right now too.
The more he sees you being liberated the more respect he will have for you too! That could be a turning point in your relationship with him.
I lost my own self trying to 'fit in' here but that was my biggest mistake. Once you 'lose' yourself some respect from others goes along with it and manipulative people hone in on that. SD pushed buttons I did not even know I had! I switched them all off and the change in her was dramatic, no more bullshit because I did not respond the way she wanted me to. Changing your responses is not easy though, I got caught off guard a couple of times but my sense of self came back toot sweet.
Do you have hobbies? Once the kids are settled for the night and you have done all you choose to do around the house then think about what you would like to do for the evenings...I write, sew, knit, crochet, chat with neighbours and friends on facebook. Whatever it is you choose make it something you enjoy doing. Once you make some friends maybe you can go out for the evening with them? DH can take care of the kids, they are his too! Getting more social is important to mothers of young children, I believe it helps the children to become more social and adjust better in school environments too.

OK, co workers means you are, or were, working...right? Male friends do not always want something in return, unless you have actually asked them and they have said so then it's an arrogant assumption that they'll 'want' something in return...how about a cash payment? I am losing a bit of sympathy for you now that you are putting excuses in the way of your own progress. You are not as isolated as you would have us believe.
I suggest you seriously think about who you are, what you want from life and look at things from more than one perspective.

NO ONE is has to stay in a marraige they do not want to be in. You keep putting obstacles in your own way, seriously, I think you are full of it. You are a phillipino then? Married to an american man?? You have as many rights as an American here if that's the case. Take charge of your own life and do what you need to do. You are married to a man who has alcohol problems, you cannot leave the country or state, he is not leaving so it's up to you BOTH to iether work it out so you stay together or work it out so you separate. I understand the difficulties facing you with two young children, I also understand the feelings of isolation in a new country. Is your husband manipulating you or is he just doing what's best for you right now under the circumstances...those being you are not feeling like yourself lately?? Only you can answer that. Get some counselling! See if you can boil the issue down to the root cause? Why are you not happy with what you have right now?? Is it because you feel insecure that he's going to spend time away from you and the children if he goes to visit them?? You do not want the SKids at your house so what's he to do? Seriously, They are his kids, have a think. Is it because you do not want to spend a broken night with your little one waking up constantly? Does your husband usually see to the baby? I am speculating here, I am aware of that, but the root cause eludes me because every solution seems to cause you more problems so the only way forward is for you to look inside of yourself. A good counsellor will be able to be much more discerning than any of us here, he/she can meet with you, understand you much better as a person and help you to figure stuff out that's best for you and the children. A counsellor can come to the house too, so you do not need to worry about transportation. How do you get your groceries? Does DH drive you places you need to be? I do not drive any longer here, I do not have a US license so I'll have to figure it out as and when the time comes for me also. I can get a ride anywhere I want to be, all I need to do is say where I want to go and it's a done deal. I might have to wait a few minutes until DH is finished what he's doing at the time but I still get to go. I am happy that most of the issues DH and I had are resolved and we are making it. Be happy within yourself and it will project onto him. I have always been content with what I have that is good and I speak up about what I encounter that is not good. It causes fights but sometimes fighting is a way of communicating and getting feelings out into the open so that they can be resolved.

Military or not he's not allowed to use his skills in civvy life, like a boxer cannot use his fists outside of the ring. You really do like to put obstacles in the way of your own progress, no one will be able to advise or help you if you do not stop obstructing yourself at every turn. You married an American, it is your choice, I married an American too, my choice also. I choose NOT to lose myself in all that being married and a step parent entails. I think you are not going to find a solution unless you look inside of yourself. I do not know what to tell you! Maybe you are the one in denial, not your husband?

All this because you want to drive a car? Where do you live that an instructor cannot come to you? What does your husband do for a living? He can take care of the kids for an hour or so while you take lessons surely? I am struggling to understand what your real issues are. You have been with this man for some years now, he drinks, he's manipulative, and tries to isolate you. There are ways to outthink these types of people, pay attention to what he does, how he does it, and you will see a pattern. These types do work to a 'routine' and someone who breaks that routine can throw them off in a tailspin. He'll go out and get drunk once you seem to be 'on to him' but he does that anyway...right? He needs a gradual learning curve, so do you! Fill your life with the kids and stuff that pleases you. Save up some money because you will need it and get a taxicab if you really need to go somewhere and he refuses to drive you! I think one of the mistakes you might be making is asking for permission from him. You do not need permission to enjoy YOUR life, tell him it will make life easier for when the kids start school if you can drive, it will make groceries easier, visiting his family easier...less of a work load for him...something...anything!

If you are a military spouse you can go to school and get help with it, you can learn a trade and study online from home. Your main issue seems to be that you want to learn to drive and that you do not want to see your husband go to his kids overnight, if I recall correctly that was what the fight was about.
You have all manner of options open to you as a military spouse, do you live on a base? The commisary is duty free. I have a military ID that gets me on a base to shop and I get discounts at stores too...bonus!
Mainly, military type guys do have fixed attitudes, they may not know any other way to be! You can take the man out of the military but you cannot take the military out of the man type thing. Your healthcare is taken care of with ChampsVA, if you live on a base then everything you really need is right there. To to a site called military.com and you can see a list of all the benefits and you can look at options available to you.

http://www.military.com/spouse

So he's not in the regular military, http://www.military.com/NewContent/1,13190,Reserve,00.html You can get a lot of general information there. I doubt he is withholding anything from you but it's always good to be in the know.
SD says these things because she knows she will provoke a response in you, stop responding! DH needs to get his head out of his ass and deal with issues. The more you mention it the less likely it is to happen really. He'll avoid the issue until such times as he needs you to be driving!
I don't know what to tell you really. Do you have a social security number to get a driving license with? The test is something you can study for at home online. The physical driving is just a basic drive around the test center, doing a couple of turns and parking etc. Study now for the written test so you have more confidence at the time you can take it. I do not hold a US license, I do not drive here. I would be looking forward to the day you can do it, stop mentioning it to him for now. In fact, look like the whole issue is a non issue. Carry on being your usual sweet self, you are sweet...right??
All good things come to those who wait, patiently! The longer you are malcontent about it the longer it will take to materialize...right??