My sister won't forgive me for breaking a promise to our dad that we'd never put him in a care facility.

I am in a similar situation with my mother in law. She has lived with me for 17 yrs. In the last 10 she has become totaly dependant on me. She requires 24/7 care. With only the help of my husband and my three teenage sons, I have been able to keep her at home. My husband has always promised her he'd never put her in the nursing home. However, it has come to a point in my life where I cannot physically or mentally continue staying at home with her. My sister in law won't help nor will my brother in law. Everytime I talk to my husband about the issue, he becomes angry with me and just doesn't understand why I would want to do this to his mom. I am your clasic burnout caregiver and don't know how much longer I can do this. How do I help my husband soften to the idea of moving her to a nursing home? I'm so tired, depressed and lonely. Just tired of fighting this issue by myself.