I have a male and a female cat. They hate eachother most
days but sometimes he gives her a kiss. Just like a man.
My little Lucky (only 3 legs) puts the run onto our male and
our daughters male when outside.
I say give them time. Let them find and choose their own space
It will happen.
NO don't put a dog in the mix. It'll drive YOU nuts. Just be
patient with the cats.