Does a family member "have to" take care of an elderly family member, or should it be "wanting to" take care of this elder family member?

Just FYI if your mom hasn’t been in the country for more than 5 years, it DOES not mean she is subject to a 5 year wait period before she is eligible for government assistance/Medicaid. Each state has its only rules about citizenship. Some states waive the 5 year wait period.

You said "where she is from". Has she been here longer than five years? Because if not, she will not qualify for any help thru the state. Can she go "home" and have family take care of her or help place her in a NH?
If she has money maybe an AL. Will husband support you in not wanting to be MILs caregiver?

Yes, you are burned out. I too am the main caregiver for 92 year old MIL, CHF and I've noticed since her second incident in 1 year (MI last September) it took alot out of mentally. Hospice and cardiologist believe lack of O2 at the time. If you feel that you can no longer take care of her, and in laws will not, start looking into long term care for her. Taking care of our loved ones takes a huge toll on the caregiver. Does your DH help hands on or are you like me, you're it. Some things I believe that I should be the one to help her with if anything for her pride (emotional wellbeing)and comfortability since I'm sure she really doesn't want him to help her shower or with other "personal " help. If the siblings have not been helping they're not going to start anytime soon. Sometimes the mental aspect is harder to deal with than the physical depending on if you get emotional support from others or not. The person you are caring for can also become abrasive towards you and even tho you know it's not them, it still hurts and wears you down. This along with all their other demands on top of your own family's demands make for a lot of work. Physical and emotional stress will affect your physical wellbeing, I've gone from a snug size 8 to a loose size 6, did I mention I'm 5'11". Good luck with everything, try to take care of yourself, easier said than done, if they aren't willing to help it may be time for you to stop. I haven't hit that wall yet but I'm sure I will someday.

Missed
you are suffering from burn out. It happens to most of us, if not all. Tell your SIL/BIl It’s time for them to step up.
Good luck.