My sister took mom out of her senior center and now treats her like a child. What can I do? I never feel welcome there.

Abusive? No matter what your moms cognitive abilities are, she must always be treated with love and respect. If you do not feel this is the case, take action to protect your mom, become involved in her care. It is often difficult and stressful to care for an elderly loved one. Give your mom a safe loving environment, if she is having issues with dementia she may be confused and frightened in a new place.
Depends. If your mother is cognitively intact, then discuss her situation with her directly and find out what her wishes are. If she wishes to stay with your sister, it is her choice. If not cognitively intact, and you think your sister is not giving appropriate care, you can try to find a geriatric social worker thru your mother's physician to get advice. If the care is abusive, it must be reported.