We had carers coming into my DP home, 6 times a day, to cover them both. I was staying there at the time. I found the carers constantly deferring to me to answer questions, lead on care giving etc, even though I had told them to just get on with what they needed to do. On the rare times they did delivered care by themselves they would come and update me on every single little thing, rather than when they were leaving. And they were good carers.
You have observed live in carers from a distance, in quite a different circumstance to that of you DPs. Whatever is arranged for your DF he will be discombobulated by the change - carers living in, your DM moving out (must admit never heard of this situation), moving to a care home. Let your DM and Dsis lead on this - they are there day in day out. It's fine to talk through options, but don't push too hard for your view to be accepted.
My DF was totally exhausted by the responsibility of caring for my DM at home. It was the low grade constant worry, especially over night that was the real backbreaker. I do understand you are trying to respect your DF's wishes, but there comes a point where you also have to consider the welfare of your DM, and that it may be in direct opposition to your DF's needs and wishes. Your DM is probably at this point - let her lead on this.
Re your DM moving out - it sounds as if this was the family home so she would have lived there many years. You don't just pack a suitcase, call a taxi and leave all in the space of an afternoon. She will want to sort through her things. The whole downsizing exercise can take weeks at best. And she needs help with caring now.
Say you persuaded her to go down the live in carer route - this too can take weeks to set up - interviewing the staff, finding the right staff, sorting out their living space. So bedrooms and bathrooms will need to be cleared at best, reburbished possibily, rotas set up, cupboard space in the kitchen found. And remember she wants, she needs help now.
With your DF going into a care home, which will also take time to set up, your DM will have time to sort the house and downsize at her own pace. She can take a breath before she moves.
My apologies this has turned into an essay. Maybe this shows just how complicated caring for someone with dementia is. There's never a perfect way, just the best you can do and different solutions suit different families.