If you are having problems with cats not getting along, I would not add the stress of a dog at this point. It might make the situation worse. IMHO

I'm wondering if the attacks are some way of mourning the cat you had to put down? Or possibly they are re-sorting out the pecking order?

Jack(6) likes to attack Dusty(16) frequently, mostly I figure it's because she's getting older and crankier. Sometimes I have to put Jack in a room all by himself for like 15 minutes, sorta like a time out. Sometimes that helps for a few days.

Try calling your vet and see if they recommend anything that might help.

Good Luck