Is there anywhere that I can bring my mother with Alzheimer's if I want to take a short trip?

Many of the assisted living and memory care facilities would accept a short term stay (1-2 weeks). Of course it was self pay.

Check with nursing homes around your area, as well as Assisted living facilities. A lot of them offer respite care.

You will want to go see them and get pricing, length of stay required minimum and maximum. Ask and get in writing exactly what the service covers for the fee.

I hope you find some place soon and get your break.