Could dad moving in and out interfere with mom's successful transition to the Alzheimer's Facility or present other issues for her?

Briefly, one month ago Dad recently moved Mom to an Alzheimer's Facility because in home care was too much of an intrusion despite heroic efforts by the Agency to maintain his own independence. Mom is still ambulatory, but very incontinent and very challenged to communicate verbally. She still knows all of us. She has always be a quiet compliant person but recently began to lose her "filter" re: Dad's constant criticism of her in her presence ("accidents", dribbling food, etc.) and would snap back at him. Mom's transition went well. She's asked to come home but doesn't push it. We feel that she's actually relieved not to be under Dad's constant control and judgement. After moving mom in, Dad got lonely and I think is feeling guilty (we pleaded with him to consider the likelihood of this). He has no friends and zero outside interests and refuses to try. Then he had a small stroke and spent a week in a rehab facility. He is leaving with almost a clean bill of health and few restrictions. He initially agreed to a few hours of professional in home help each day and I also offered to stay with him until he was comfortable. I wouldn't say dad is sharp as a tack mentally, but he's darned close. Mom has been asking where he is and not quite buying our explanation that he's not feeling well and will be back as soon as he's better. Mom's new Alzheimer's Home learned of his imminent release and asked if he'd like to move in for 30 days. He's thrilled because he gets to be with mom as he continues recuperating. He will not share a room with mom but spend most of the day with her, meaning she won't participate in as many planned activities (because he won't). She'll be seeing my Dad use a walker for the first time and will know that him living there means something is really wrong. It's a new facility and not even close to full. There are maybe a dozen residents and there is only one that Dad has anything positive to say about so he won't want to be around them. Mom spent a few days this week in the hospital due to a fainting incident with a brief convulsion and her overall strength and activity level has declined in the last month. My dad won't consider a respite stay anywhere else.

I'm wrestling with several things. I would value the benefit of your personal experience: 1) Do you think this will have a positive or negative effect on mom's "settling in" at her new home? 2) Do you think a second separation in 30 days could accelerate her decline? 3) The Director of another facility we considered for dad was shocked that an Alzheimers Facility would allow this, much less initiate it. Does this seem responsible? They haven't been too receptive to us trying to fill them in on dad's behavior toward mom.

It's nice to have some objective opinions on this. My siblings are divided on whether this is a good idea. I'd like to get comfortable with it and feel I need to advocate for mom who doesn't have a vote.