At-home care and insurance?

The most viable way to prepare for it is through long-term care insurance, however, if you don't have the budget, it may not be the right fit for your mom, because long-term care insurance rate as discussed is quite expensive.
VA- care providers vary in their qualification for benefits. Eligibility is not exclusive for disabled and individuals who engaged inwartime , check with you local VA which programs your mom might qualify
Medicaid - does cover home care but it is limited and requires you to pass some criteria, you have to call your local office for ystour ate's medicaid program.

Mobile home: they can put a lien on it.
VA- does not have to be a disabled vet, just a wartime vet.
Managed Care--- is mandated for Medicaid recipients in some states. Very often it does NOT mean leaving her residence.

So there may be literally no options? It's awful that they cannot keep older people at home. I would never want to stick her in one of those homes unless she required advanced care. I'm very worried about this.

She wil be buying a mobile home. Can they take it?
She is not eligible for VA as far as I'm aware, as her husband was retired from the service, but not disabled.
"Managed care" - does that mean she would have to be in a home? I don't want to do that to her if it can be avoided.

Your option is Medicaid. Some states require managed care for Medicaid enrollees now. Check your state rules, I don't know where you are. If she was married to a wartime vet, she may get VA Aid & Attendance if her MD certifies her need for services at home.
Avoid reverse mortgages, many lenders are extremely predatory or turn around and sell the loan to an aggressive collector.
Long term insurance is outrageously expensive and the benefits are limited by either time or dollar amount or both.