Hi, Tango, and I am sorry to hear about the situation with your mother. You all must be stressed and upset by what is going on.
I wish I had brilliant advice but can only offer sympathy and what I've learnt here on TP and in my support groups and workshops.
I would suggest some kind of support for you, and if your dad would consider it, for him also. I love TP but have also gotten good advice and information from various support groups, carer's cafes, and workshops. I imagine that Age UK and/or the Alheimer's Society, could point you towards what is available in your area.
It sounds like your dad is at least as much a worry as your mum. I wonder if you could get his GP to talk to him, if you think it would help him to hear a "voice of authority" tell your dad that for his sake as well as your mother's, your mother needs the care? Just a thought. Sometimes an adult child is not the right person to deliver advice or suggestions to a parent; they sometimes listen better, when someone else tells them. I also wonder if your dad needs checking or treatment for depression or anxiety or any medical conditions. As you mentioned he has heart trouble I wonder if he could be having physical symptoms or problems from his cardiac condition, that are making him feel worse. Or perhaps he needs a companion or carer to come to the house, for him?
I also wonder if there is some routine of calls or visits between your parents, that would not upset your mother, but would help to calm or reassure your father.
I can give you a very sympathetic shoulder on the not settling and being hurtful front. I would also say to give the situation longer before deciding it's not working; 4 weeks is not very long. Opinions on visiting or not visiting vary and it really depends on the person, their dementia, the family, and the situation in general. Not visiting is what worked for me. After moving my mother to her care home my husband visited, but I did not visit my mother for almost two months, as my presence agitated and upset her and wasn't very pleasant for me, either (and I'd been through all kinds of awful with her in hospital for two weeks prior). Then I started making short visits, never alone, and gradually I was able to make the visits more often and for longer periods of time. A year later, it's fine, although I still mostly visit with my husband.
But you and your family have to do what works for your mother and is best for her. I would talk to the staff and ask how your mother is on a day-to-day basis, so that you have more information, and reliable information, about how she is doing and how she is settling from the staff's point of view. My mother has Alzheimer's and very poor short-term memory and her version of how she spends her time is not accurate, to say the least.
Again, I'm sorry this is so difficult and upsetting for you and your family. I would definitely see what kind of support you can put in place for yourself and your father. Best wishes.