Should mom be placed?

Mom has dementia/Alzheimer's. It has been escalating for the past say, 5-7 years. There are 2 moms now. The first I would place in a heartbeat. I am afraid of her when she is in this state of mind. She is emotional, agitated, inconsolable, hallucinating, delusional, downright mean. Physically she is unable and unwilling to be mobile and unable to control BMs and bladder functions.

My other mom is pleasant, smiling, happy to see me and talk about her past. She understands she needs help and says she appreciates all the help given.

My dad (87) is her primary caregiver. He has always been a patient and logical person, but it is taking it's toll on him. I help him as much as I can, but I work full time and am single taking care of my daughter and my house, which is a challenge all in it's own.

My gut tells me to put the first mom in a home where the professionals can handle the challenges.

But I just keep picturing my other mom (the mom I know and love) to be so abandoned and confused if we move her to an assisted living/nursing home.

Help!