I'm going on vacation. Who can watch elderly mother?

If your Mom is living on her own, but needs care, you could schedule paid caregivers to come by 3-4 times a day. I have done this before and it works well...of, course, Mom already knew the workers and liked them.
Maybe you could do a trial run at any facility or with paid caregivers to see how your Mom responds. You do not want to go on vacation and be called back because Mom doesn't like her lodgings.
good luck

Many nursing homes will do respite care. This would allow you the freedom of going on vacation without worrying. You could contact your local Area Agency on Aging, often they can help. They can make referrals for you and help you with what is available in your area.

Have you looked into adult day care? Some centers will take an elder for an extended period of time, so that the caregiver can go on vacation. to find adult day care in your local area, use the AgingCare provider guide:
https://www.agingcare.com/Find-Senior-Care/