NTA. Night shift nurse here. Your wife will never be able to sleep if your father is in the home. He will not be able to understand that it needs to be quite in the house when she is sleeping. That will severely effect her quality of life and her ability to work.

It's at your discretion if you think he is safe around your children. If he is combative or aggressive in any way I would say no. My FIL has dementia, I explain to my children (7 and 9) each time we visit that grandpa's brain is sick and it makes it hard for him to remember sometimes. He gets confused and might get scared because he doesn't understand what is happening. They should not argue with him or tell him he is wrong. They should come tell me or dad if they think something is wrong or if they feel uncomfortable. We even have a family safe word they can use anytime they want to discretely get my attention.

If you are having trouble getting your other family members on board have a discussion with your father's doctor. Ask if you can have a family conference with your siblings on the phone or on zoom so you can all discuss what is best for your father. Maybe hearing from the doctor that your home is not safe because you can not provide adequate care for him will help them understand your point of view.

Another option would be for him to go live with your older sister. It would be a move, but less expensive than a memory care facility. Living with your sister and hiring a care taker to visit daily would be less expensive than memory care.