I have no idea about the cats - that's likely a question for the Cats forum. LOL!
Regarding dogs, I've always been told that a male-female combination works best, but that theory has been busted in my family. Any combo works, and it's more due to the individual personalities than gender.
We've got 2 birds who spend all their daylight hours out of their cages. The dogs all accept the birds as part of their pack, and I trust them all not to harm them. Our ancient cockatiel just loved our first dog, Travis. He followed that dog all over the house, and even cleaned his toe hairs and whiskers when Travis was laid out on the floor napping. LOL!
We also have a lot of animals. Two big dogs and four cats...the latest addition is a 7-week old kitten rescued from a tree last week :-) When it comes to getting along, I think it all depends on personality, like Jaybay said. All our animals are female, except one male 3-year-old cat. They all pretty much get along, but our oldest cat, who's 10 now can be a little grumpy and is not quite as social as our other animals. However, of all of them, she gets along best with out other 3-year old female cat. So who knows?
Funny thing, though...after we brought the little kitten home last week, the one who's the most interested in her is our shepherd mix dog. We're keeping the kitten separate from our other animals for now, but our one dog is constantly sitting outside the room we keep the kitten in... She's even whining, wanting to go in there. She loves cats, though. In the winter when it's cold, she actually lets our cats curl up next to her for warmth. Too cute!
Oh, I do have one question for you, though. Is the new cat young? If so, that could have something to do with it. Maybe she just has a little bit too much energy for your older cat. Their relationship might change when she gets a little older.