My husband and I are his mother’s full-time caregivers.

I would say if Mom is on in home Medicaid, she has no money to pay for respite care. And you seem not to want to pay outvof pocket, but thats what u will need to do. It probably will be cheaper to find an Assisted living that can take her than pay for 24/7 care. Maybe a nice LTC facility. And u need to discuss this with Medicaid, you should not be receiving pay while away. They may also pay towards respite care to give u a break.

SHE pays for the Respite stay. You do not.
So yes it is out of pocket and I guess it is a matter of semantics who is actually paying for the Respite stay. It is for her care so it is her expense.
If she is on Hospice then Medicare/Medicaid would cover the cost for about 1 week of the Respite.
You do need to plan ahead as there is a lot of paperwork that goes into respite. She will probably need a doctors form filled out indicating she is in good health and any and all medications she is on. And you will probably have to have her get a skin test for TB this can also be done as a blood test. If you do the skin test some areas require a 2 step test where the test is repeated so that needs about 2 weeks.

Respite service is, yes, out of pocket paid. And not cheap. I would keep checking for the best deal you can find, but do know that this will be costly.

I am hoping that you have a good contract with your MIL for "shared living expenses" because some of her SS funds should be coming to you for shared cost of mortgage/insurance or rental costs, food costs, and etc. I would see an elder law attorney re all this and your POA pays for that expert advice from your MIL funds. While "rental" is reportable to the IRS as income, shared living expenses usually are not; so use the visit to elder law person to work that out as well.

This would give you a bit of an account for respite care costs so that you can get that much needed vacation.

Good luck.