When I first got Mikki the first week was HECK!! Mikki was not spayed at the time. She was being very aggressive and Rosie was having no part of it. I continued to break them up when they fought. Finally, my groomer told me to stop. She said let them figure out who is who. I did this. Rosie pinned Mikki and showed her who was the queen of this household.
We still have spats but not the true fights like we had at first. Plus Mikki was spayed. That helps a lot!!
They do still fight for our attention. I try to give attention equally to them. Or if I have one, I have DH play with the other one. They don't act like they like each other much when we are home. But my son has caught them sleeping on the bed together curled up next to each other when we were gone. So, I think they like each other more than we know!!
Everyone told me to do for Rosie first and Mikki second when I first got Mikki. Rosie was 4 years old and Mikki was 1 year old. To this day, Rosie still gets her food first, gets picked up first when I come home, gets treats first, etc. I hope more members that helped me can come on here and give you the same advice.