Dad is on Medicaid and Mom lives in family home. If Mom dies, how soon will the state take her house?

The house is an exempt assets under Medicaid. Your mom is considered the "community spouse" under Medicaid rules and as such will qualify for the community surviving spouse exemption to an MERP - Medicaid estate recovery after dads death. But if mom goes & sells the house right now, then the proceeds from the sale will likely cause an increase in dads assets (as the house is 50/50 community property) that will cause dad to be in eligible for Medicaid.

You probably don't want that to happen. See an elder law attorney before mom goes to change any ownership or sale of any assets.

Medicaid will never force her out of her home. She gets to stay there as long as she is able to. With your help now and then, she could be there another 30 years. State subsidized housing is usually on a sliding scale, so the rent varies with income, and the tenants are very low income, usually welfare.

If Dad dies first, Mom can continue to live in the house until she dies.

I think it would a good idea to consult an attorney specializing in Elder Law regarding the other possibilities in your state.