Tips to get nursing home care, how should we proceed?

Hello, My father in law is 90 and really needs round the clock care. He lives with his ex-wife out of convenience, but she is unwilling to care for him anymore. She's 85 and lacks the strength as well. He is dual eligible and I think we can get a home health aide via MLTC, but the ex-wife doesn't want a stranger in the house. We need some help figuring out how best to proceed so that he can get admitted into a nursing home so that he gets the care that he needs. I should mention that our financial situation means we are relying on Medicare and Medicaid to fully cover the costs. Thanks for anything you can share.