Should I sell my father's house and bank the proceeds until he passes away?

I put the money from Mom's house into two CD's, one was a six moth CD and the other one for a year, then I renew them both for a year when they come due. That way one comes due every six months. You could have four CDs and work it quarterly. Make sure you have durable POA and you can also put a POD on the CD's. They aren't making much right now, but it's better than a savings account and keeps people out of it. Good Luck.

If they were to sell now or in the future, where is the best place to put the proceeds so that they are accessible for NH care in the future if there is no trust?

I would also talk to an elder lawyer since it is in trust it can not be taken for NH fee if it is sold I do not know-could you charge her rent or just rent it to someone else for now and the market for house will be down for a while yet-but a lawyer will be able to help-you do not want to make a mistake and have to pay big bucks down the road.

I would talk to a lawyer. Would the money from the sale still be protected by the trust or is it to be used for his care eventually anyway? If so, I would give the girlfriend notice and put it up for sale or if you think the market will improve, rent it out (I assume she's living there for free). Best Wishes.