I have no issue with your husband's ex getting child support.  Children are entitled to be supported by both parents.  The fact that the mother is rich doesn't excuse the father from supporting the children.  I assume that he's paying the court ordered amount in your state, which presumably is based on his income.  Your husband should feel lucky that he didn't have to pay child support for years.  His ex-wife's motivation for asking for child support seems suspect, but the kids are entitled to it.

Do the twins listen to your husband and only defy you, or are they defiant with him, too?  Does he parent them? Do you know for a fact that the BM tells them they don't need to listen to you?  Does your husband speak French?  Have you spoken to your husband about your frustrations?  I wouldn't count on him seeing that you're tense and on edge; if you haven't already, let him know that, let him know why, and let him know it has to change.  He needs to put an "English only" rule in place for your home (it is RUDE of them to speak French when you don't understand it if they are perfectly capable of speaking English) and he needs to set behavioral expectations with consequences if they are not met.  Of course he will not want to for fear the children won't want to spend time with him anymore.  At that point you will know this is a husband problem.

I hope things get better for you. I feel the same way about my skids. You have a DH problem. It really doesn't matter what BM says it is your house and you need to take the control back in your household. You don't give kids choices to do whatever they want to do. Your DH needs to understand that his kids don't run the show. Or you can disengage like I have. Stop doing thing for your DH and his brats that might work too.

I am going to be super honest here and apologize in advance. 

For around 10 years your husband had twins that he had no interaction with. No child support, no visitation, no nothing. He never saw a ballet recital, or softball game, never went to have lunch at the school, never was a part of their lives. Then all of a sudden, Daddy and Stepmommy with 2 kids that they just love show up and these kids are thrown in the mix. You are mad because they are resentful?? For real??

Of course their mother undermines what you do. She did it on her own for 10 years. She had all the sleepless nights with twins, she had all the doctors appointments, she had all the activites, she did it all- and the girls are bi-lingual!  And without any financial help AND is a lawyer. Yeah, I don't even blame her. 

I have sympathy for everyone in this case - minus your husband.
He is the cause of a lot of the problems here.
You seem to blame the skids and the BM, but not your DH.
Look a bit closer to home as to how these problems came about and you will find your husband at the root of it.

I don't want to rehash history or beat you up but  the situation is difficult.
You not wanting the skids around or asking your DH to refuse visitation with these kids is going to prove them right: their Dad can pop in and out of their lives when he wants to.

It seems you are trying to make this work - and no one is helping you.
Why do you not have a sit down meeting with the twins and your husband?
Why do you not explain to them what you are trying to achieve with visitation?
Explain why your house rules are different.
Ask them to speak English, not demand or enforce that they do.
It appears that French is their first language, they speak it to each other, ask them out of courtesy to speak English.
Further hostility to these kids  about language only gives them reason to defy you.

Have you asked BM to help you with adjustments in your home?
Or has it been an expectation on your part that she would do this?
Surely she too can not be happy that her children need to spend time in an environment where there is conflict?
Maybe if you approach her as a mother, she may be open to helping you.

This woman has raised these kids on her own for ten years plus.
She is a lawyer and would know she has to allow visitation with you: she may be open to helping make it less of a battle if you ask her, and I am not sure you or your husband have approached her on  this?

is that the kids adapt to the adults and not the other way around but I think in this case some compromise might be in order. This isn't a typical step situation. I am not saying let the kids run the show, but for example, learning a few recipes the kids like, asking them what activities they prefer, etc would go a long way. Possibly even asking them how they are used to eating. For example, if they have been raised with a traditional French meal schedule then they eat a large meal at lunch and a light dinner. A heavy or large dinner might not even appeal to them. Little things. Little adjustments that actually make them feel welcome instead of like they are squares being forced into round holes. 

You could ask them to teach you and the younger kids French if they agree to speak English while in common areas of the home. 

You say you want them to be part of the family but your expectation was that two preteens who have been raised in a completely different way from your own kids would fit into your family with no regard for how your husband could fit into their already long established lives. 

A lot of custodial parents let kids about age 14 decide to not come for visitation. Maybe this will be the case for you and your CS payment will be the small fee for the freedom from stress when they visit (or decide not to).

It just amazing how people see thing with rose color glasses.  Your DH did nothing for ten years, BM supported there kids by herself, had sleepless nights with sick kids without help.  Had to do Christmas, Birthdays by herself. Paid medical insurance and other bills by herself.  Now your DH want to be the fun dad, with ten year olds,  And want to do it for free.  And you can’t see why SK hate you.  DH wasn’t around when BM spoke french to her kids, but now you don’t like it.  You don’t want to pay CS, or be nice  to SK.  Don’t get the fact that SK don’t want to be at your house !  And I don’t blame them.  Nobody likes, Jonny comes later!  How do they know when you are going to stop having them.  That what you are leading up to

One question. Why should SK respect you?  What did you do to earn respect.?  Why would SK even want to be around you two?  They are 12 they know how they were treaded. They remember, when they were the only ones with out a father at events !   Then you disrupted BM life and call her crazy.  BM was doing fine for ten years without you two and now she got a  non caring SM to contend with.  

You were a SM for five years and never saw SK. I am sure you made excuses for that too. 

I think you need to not be so involved with the twins and let their dad deal with him since that’s what he wants to do so badly. Take care of your own two and don’t get involved with them when they are there. Do all your errands and fun activities for yourself when the twins are there so that you don’t have to spend time with them. Don’t force family outings that include the twins. Take your own two to do things when twins are at the house. Let DH spend time with the twins alone. I avoid skids like the plague and let DH take care of them on his custody days. If he wants to do stuff with me he has to leave them at home because they are not invited. They also don’t follow rules well and are defiant.

But honestly, no visitation for TEN YEARS?! How difficult must it be for the kids to HAVE to go stay with STRANGERS for the weekend? 

After not having visitation for so long, while he may be their "father", he is a stranger. 

I feel bad for the kids. Why after abandoning them for 10 years did he decide he needed to be in their life?

I can see the kids point of view, he acted like he didn't want them for 10 years, meanwhile had more kids (that he wanted and took care of). Of course the kids are going to be resentful (and probably very jealous of you and your kids).

I understand it’s hard on you.  But your DH -even with little $, and even if he had tomove for work - didn’t appear to keep up with calling his children, or do as some do and write letters, send cards for milestones, taking a photo of what he sent to show he tried to keep contact.  If he did do something - anything - but what appears to be abandoned young children, then my apologies.

Look, I realize this is hard.  My SO has a bonkers, and cruel ex.  She has done so much to alienate them.  But through all the painful times, he kept up contact, and even when laid off sent CS, even if not the full amount and made it up as soon as he could. Heck there were times he was to get them and she would pull antics refusing to let them out of her car, and he would still let them know through a closed car window that he loved them and would see them soon.  It was heartbreaking.  But now in their tweens and teens they love their dad, and understand their mom is the issue (because in reality she treats everyone in her life poorly, down to her own parents).

So these poor  twins abandoned and now forced to play happy family with a man they don’t know, and a woman who clearly resents their presence, deserve sympathy.  At 12, they don’t have the life skills to work through this.  Even in your home, your DH abandons them with you.

Frankly, until your husband does some real work getting to know the twins, apologizes for leaving them high and dry, your life will continue to be miserable for a few more years until they are old enough to just say no to visits.

If you want to help, do as others suggested and make yourself scarce.  Don’t put your own children through this.  Let your DH deal with the very reasonable reactions from two kids he didn’t care about for years, and literally replaced with your own.  Ultimately only he can work on repairing whatever can be salvaged with the two twins.