So I'm going to try my best by breaking this down

- adult stepson is a vegan

And that's all fine and dandy but he's an adult meaning he or his father should have options to eat in the house. It's not on you to go and buy extra crap for him. If you serve a meal as a family give him an option ( mashed potatoes are easy to make vegan ) and thats it. His lifestyle , his choice, his issue

-The kids being in all common places

Can dad take them on a hike for awhile on your weekends ? Great bonding for them great house time for you.

-As far as having another kid

I'm in the same boat. Do what feels right for you. Part of me would love to stay the younger childless stepmom but another part of me wants a kid of my own.

There's really no right answer there to be frank. Also you are a damn sweetheart because you have been cooking and cleaning for no reason.you have been catering to these kids for no reason. I think you need some you time. The kids can make their own food when over . Relax and let DH handle it. Read a few books. Enjoy life  

I make a huge effort to cook them well balanced meals that they enjoy (I HATE cooking)

the 19 year old, actually, who's also a vegan, is most annoying. This also means I must find special food for him and cook him special vegan meals

Well, this jumped out at me, as it is not your responsibility to feed them, especially the vegan 19 year old. Who, by the way, is not "just a kid".

I have to be responsible for them....cook their meals, wash, clean up after them

No, no you don't. Who told you this?

You are not responsible for taking care if these kids, period. One is not even a kid.

Do you want kids? I mean, really want kids? If so, that's a different conversation.

I have never wanted kids and my husband never expected me to take care of his. Your husband should be taking care of his own kids, period.

Can I ask how old your DH is? Is the real cry for own child what's really happening? (I wrote a blog about my story recently) As I may have skewed my SO.. he does say the same things like "I'm almost there" when it comes to being "done" parenting. 
 
I am with the other posters as what should come from the 19 year old. If he doesn't want what you cooked.. he makes his own, can't pick up after himself.. DH does it.. and so on. 
 

I also fear this about my SS16. Time is starting to crunch and college is NOT in his future, no goals are set, etc. hopefully this kid joins the military. 

Do you have shared finances with your DH? If you do, you should consider separating finances, then leave him to feed his ‘kids’ however he sees fit. It is NOT your responsibility to feed these people, the 19 year old especially is old enough to cook for himself. They all are, really, though the 13 year old would likely need some help. 

The fact that your DH is brushing this off as ‘they're just kids’ is a red flag... they aren’t just kids. One is legally an adult, one is nearly legally an adult, and the other is a teenager. All of them are old enough to contribute to the house, these aren’t infants or toddlers running around. You’ve got a DH problem big time. 

Having your own kid is the biggest issue I saw in your thread though. Your DH clearly doesn’t want another baby, and you seem like you do. If you stay with him & remain childless, are you going to be ok with that a couple decades from now? Or will you resent & regret not having a baby of your own?

I’ve got an infant, having your own baby is nothing like having skids. Not even sort of the same thing. If your DH is telling you having a baby is horrible, then he’s either telling you that to convince you not to want them, which is wrong, or he just doesn’t like the baby phase. But it’s not all horrible, I love having a baby around, and I would never tell someone who’s considering having their own not to do it based on my own experiences. It’s such a personal choice, your husband is wrong to try to manipulate you that way. 

If you want your own kids, I’d be reconsidering this relationship. Honestly, if your mental health is as bad as you’ve described where you’re crying in a closet when they’re there, you should be rethinking it anyways. Your husband needs to step up, stop doing his job for him, and if you want a baby find a way to make it happen, whether with him or someone else. 

Two things.

1. Stop cooking for the vegan. He can eat what you make or fend for himself.

2. I am a stepmom who recently had a first baby. Let me tell you, there is no comparison between a skid and your own child. I love my skids, but it is not the love I have for my baby.  If you want a child, have one. 36 isn't that old. Don't take the skids into account - your child will not be like them. Do not give up having your own child - if you want one - because your DH would rather not. He HAS his children, and you've put up with them. If you give up having a child when you really want one, you will resent your DH and it will not bode well for your marriage.

If you really want a child, you need to have a serious talk with your DH. If he does not want to have a child he needs to be clear with you, so you can leave him and find someone else to have a child with. That might sound extreme, but I think the resentment of having to deal with his children if you don't have a child that you really want will destroy your relationship. He has children, you don't. Stepchildren are not the same. He can't tell you how terrible it will be unless he is willing to say that he wishes he never had his own children, which doesn't seem like it's the case.

Definitely stop feeding the 19 year old he is an adult. Only buy what groceries you would normally buy.  If DH feels SS needs special treatment let him be responsible for it. I stopped buying SDs special groceries and SO only lasted a few weeks before he realized how ridiculous it was to spend all that extra money each week.

As far as having a baby. If that's something you have always wanted to do. It is an amazing experience. You cannot compare being a stepmother to being a mother.  Its completely different when you bond with a child you conceive and carry.

He should be handling everything with the kids. To expect a woman who brings no kids to the relationship to handle his THREE kids is ridiculous.

And this is not the man to have kids with, by the way. I would say having a kid with a guy in his mid-40s who hasn't been a dad yet can definitely work... but having a kid with a guy in his mid-40s who has already raised three and really didn't even want those kids is another thing completely. His energy for that is gone, as evidenced by the fact that he's outsourcing some of his responsibilities to you. If you have a kid and he is indifferent or not helpful, you will resent him for it and you will end up either stuck in a miserable situation or as a single mom back on the dating scene after a divorce. Read through the stories here. 

If I were you I would sit down with my husband and ask that we implement 3 changes right now now.

1. He needs to do the grocery shopping the weeks his kids are with you two, he can also cook for them or he can pay for take out. 

2. He needs to give you some free time while they are at the house all the time with these lock downs. I would suggest that the boys must spend an hour or 2 in thier own rooms during the day and an hour or two outside getting exercise or maybe dad can play a computer game or some thing with them for a short time so that you can focus on whatever you want to do in peace. That will give you a break from them each day and time to re-energize.

3. I would also either start trying for a baby asap or forget about it altogether. Discuss it together and see where you both stand. 

As a 35 year old who has been off contraception for a year and still hasn't concieved, I would not recomend putting it off any longer than you have to. If the thought of not having your own kids is too hard to swallow right now and your husband is unwilling to commit to that step then I would seriously think about moving on from this relationship (and maybe looking into freezing your eggs). You talk about hoping that his kids will be less hassle in 5-10 years and you sticking it out in the mean time, when you could be out there finding someone else who is better suited to what you want in life.

You CAN imagine your life without your husband, you lived many years without him before you met him and I am sure that you were pretty succesful and doing just great without him and if you were on your own in the near future, I am sure that you would soon be doing better than ever before. 

Sometimes love can fool us into thinking that there is noone else we could be with that would offer us as good or better relationship when we know logically that that is nonesense. 

If you think you really want kids, don't let him persuade you otherwise. If you want them and he doesn't, that doesn't make you a good match.

Speaking of a good match, relationships are about quality, not quantity. A relationship that is great 90% of the time is still a bad relationship if the other 10% involves abuse, drugs, or other tensions that cause someone mental anguish.

Also, gender roles don't have to be a thing. They're a thing because people decide to act on them. You have ZERO obligation to behave like their mother. You have ZERO responsibility to them just because you're female. You and your DH need to come up with a share of household responsibilities, but his kids aren't part of that household pot. Those are HIS responsibilities that HE is responsible for 100% of the time. YOU are an ADDED responsibility to hit plate, not a crutch that he can offload some of his responsibility onto. He already came into your relationship with something he was 100% responsible for, and caring for you is *in addition* to that.

Finally, the 19 year old is an adult. If he wants vegan meals, he can get off his arse and make them. If he wants to live a lifestyle not conducive to your home and lifestyle, he can get a place of his own that he is responsible for. Your home is your domain, in collaboration with your DH. The kids follow your mutual household rules. Period. End of discussion.

Your DH does not get more say in your household just because he has kids. If this were a team sport, he's not the coach while you're the player. You both are players in different positions with different responsibilities to the team. Don't let him or yourself convince you otherwise.