Is there a program that pays someone to sit with my Mom?

I don't know what state you are in, but I spoke once with a lady who was the director of a Senior Center in the state of NC. She told me that they provided respite care for families' who care for dementia patients in their home. I didn't get the details, but I think it was free. I'm not sure how long you got the respite care. It might have been only for a weekend, but I might call your local Senior Center and see if they do something similar. If they don't, ask for a referral. Sometimes just asking a lot of people for referrals will eventually hook you up with someone who might can help you.

I don't know of any program that will give you a free caregiver for how many days you need for a trip. I see from your profile that your Mom has Alzheimer's/Demetria... if there are numerous things she cannot do for herself, you probably would need to all an agency who have caregivers familiar with memory issues. Would your Mom even allow a stranger in the house?

Is is your Mom on Medicaid? If yes, check with your State Medicaid office to see if they have a program that could help out.