Hi there, and welcome.
We've been through various runs of this - and my SIL too is a master manipulator - she can escalate any situation to neighbours, to family up and down the country, to get the attention/result/sympathy she feels she needs.
I agree daycare would be worth a try - we are having quite good success with this after a lot of effort. The secret was finding something there for her to participate in that made her feel she was valued by the staff and other 'carees'.
From talking to social workers, it is common for people to think caregivers are actually friends visiting for a cup of tea and some scintillating conversation about their various medical conditions. That was certainly the case with SIL until someone let the cat out of the bag and she promptly started booting them all out!!!!!! I don't know whether your Dad is at a stage where you could make that work? Introduce the person as a friend of his/yours and say they would love to vsit for the afternoon and hear him talk about (insert something your Dad loves to talk about).
One thing we did that worked, but that I am not totally comfortable with, was to present it as a "compliance" issue. SIL's number one priority is to stay living 'independently' - we said that everyone wanted that for her too, BUT that the doctor has said she
cannot stay there
unless she accepts the caregivers. Now, I feel there is an element of bullying in that approach - especially for someone whose disease already makes them very insecure. BUT, it worked very well.
Those are a few experiences we have had that may be of use to you, I hope so.
love
Georgie