Am I wrong for wanting to quit?

You have to quit. You can’t set yourself on fire to keep someone else warm.

You know what, he can BE cold. That's fine. I hope you made it clear before she came in that this may be a no go. It is.
I would not equivocate. If he thinks his pouting can make a difference then he will pout.
You need to be firmly gentle and tell him:
Just say "I was reluctant in the beginning and I regret not holding my ground, because agreeing to try this has made it more difficult for all three of us. But I cannot do it. I have just run smack into my limitations. If this doesn't work for ONE of us then it doesn't work. And it doesn't work for one of us and that one of us is ME. I can be as sorry as I want--and I AM sorry--but I cannot do it and I WILL NOT DO IT. So let's get ourselves together and tell Mom that I cannot. I am fully happy to take the blame or whatever you need, but I cannot do it. If you insist on continuing then it is the end of our marriage, and you will be left with all the caregiving."

As I said, if he sees his chance to have this then he will play you in his desperation. You didn't cause this and you can't fix it . Being an RN is what taught me that I would not/could not, no matter the love I had, do such a thing 24/7. Not in a billion years. And I never would have considered it for a single second. I am not applying for Sainthood. It's an ugly job description.
And no one in my family ever would have asked this of me.

Taking in someone thusly reluctantly and being unable to do it simply adds to the tragedy that it already is. But that is something you all must bear. There is no perfection in this.

Please don't try to continue this for the sake of you all.

Are you wrong to want to quit, you ask?

“We have 3 year old twins. . .”

What? No! You aren’t wrong to quit at all, you have little ones at a demanding and critical age who need to be you and your husband’s first priority!

“I work part time as RN nurse manager. . .”

So MIL (who from your profile besides the stroke suffers from incontinence, diabetes, heart disease, mobility issues. . .) AND small children on top of a demanding job? No!!

“I forgot to mention that I’m an amputee. Amputated at the knee since I was a teenager. My right leg. I have always been able to keep up and live a pretty normal life otherwise but this is too much . . .”

NO!!!!!1!!!!!!!!!

On second thoughts.. "I quit" may be the clear, direct words your husband needs to hear.

He may push back.

Eg You say you can't.
Yet he knows you are amazing...
That you are a capable woman - a mother, a nurse, caring is your role (as chosen by you & also gendered society assumptions).

If so, he needs to understand the word No. To teach his children too. That when a woman says No a man respects it.

If words are not understood, move to actions. Just as you wpuld for a patient. You say you cannot stay with them 1:1. That you will return. Then you leave.

Taking a short holiday with your children to a friend's or other relative can work wonders.
Then a husband MUST deal with his Mother himself.

OMG....You are basically newlyweds! In your 30's, and now possibly stuck another 10-20 years as MIL's personal caregivers? MIL needs care 24/7. You aren't the only skilled nurse to do this. SNF would have 24/7 care, spread among 3 shifts.

Your MIL knows damn well you have your hands full with your twins, work and are already an amputee. After a paralyzing stroke, MIL should have stayed in SNF from stroke forward. Not agree to move in and destroy her son's marriage and budding young family. She is paralyzed, but still has her mind intact...for now.

Your husband's priority should be his wife and his children. What happens if you get sick? 24/7 care for someone paralyzed is too much work added to your busy life. When do you have time to sleep?

You didn't marry his parents, it wasn't a package deal. She needs to go where she knows she should be and you both get your young lives back. Don't let it go on much longer, or you will be trapped for the next decade.

Does husband actually expect you to sacrifice like this for how long? Years?
Let him pout! He can pout his way into a divorce and child support payments.

You tried. Which was pretty noble of you, in my book.

So he's cold. You've told the truth.

He can either hire help with his mom's money, or he can look for a facility.

Does he know how to do that?

You already have great advice below .

But I wonder …….
Is your mother in law competent ?

Is your husband afraid to tell her that you can not care for her anymore ?

If your mother in law is competent and your husband does not address the problem after trying one more time to tell him you can’t do this , then you tell his mother you can’t do it . You can offer to help make the other arrangements .

If your husband does nothing to relieve you of taking care of his mother , stop taking care of her and leave it up to her son .

Your husband must just assume because you are a nurse it wouldn’t be a problem .
You are working for free , and it’s ok to quit.

Something I don't see being addressed here is the fact that Kim states she only works weekends. I mention this because I have seen this before with HC workers, We work 12 hour shifts, in a stressful job. We are NOT off the other days, we are resting and taking care of our families and sometimes the family forgets we actually are employed! My own ILs once told me I should get a job for the days I was off, like yes, of course I want to work 7 days a week! It is likely her husband thinks since she is "off" she has plenty of time to take care of Mom! I agree the kids should come first, along with her health. Time for hubs to step up, after all, he is "home all day" too!

He is showing his true colors, isn’t he?

This isn’t the first time that we have seen wives complaining about their husbands wanting them to take care of their mothers and I am sure that it won’t be the last.

You made an honest attempt at being able to do this. You found out that you aren’t a superwife/mom/daughter in-law. Join the club! No one else has super powers either.

Tell your husband that you sincerely tried but it’s not working out and that you expect him to speak to his mother about other living arrangements.

Wishing you all the best! I hope that your husband will understand how you feel. If not, you will have to figure out what the next step should be with or without your husband.

Your needs are equally as important as his mother’s needs. In fact, they should be more important than his mom’s needs. You and your children deserve to be number one in your husband’s life!

Your responsibility is not to care for his Mom, thats his. He can spend his Moms money for aides. Your responsibility is to take care of the Twins.