Cat Behaviour?

The first sentence you wrote was enough for me to understand the problem, you "introduced" them, there is no actual way to introduce cats and expect them to get along just fine. You need to look at this from a cats prospective not a human prospective, Diva is the owner of the territory (yup, she is, not you) she gets along with the dog because they have an understanding that she owns the territory, whether the dog understood that right away or had to get slapped by Diva a couple of times doesn't matter, they now have an understanding that she's the queen of the house, you and your son provide her with food, attention and love so she is more the happy to to share her territory with you But all of a sudden Sqeeks comes in the picture, invading her territory eating her food, stealing her pride and she will not have that! try watching a documentary about lions sometime, see what happens when a young lion tries to join a pride, he will fight the alpha male to death if he needs to in order to get that territory. Sqeeks is invading Diva's territory and she is willing to defend it no matter what! she feels invaded and under attack. Hopefully that will help you better understand where Diva is coming from.

Now lets solve the problem! What you will need to do is re "Introduce" them but in the right way, cats don't hold grudges but Diva does remember how Sqeeks smells and knows that smell means trouble! You need to associate Sqeeks smell with positive things. if Sqeeks has a favorite toy, let Diva play with it, let her sleep in her bed, Anything that has her Smell let Diva use so she will get used to her smell. Second, Introducing them does not mean just putting them in the same room and letting them do their thing, You need to separate them to two different areas, preferably different rooms where they can smell each other through the door. they will growl and hiss but they can not hurt each other. let them eat next to each other on both sides of the door. if they feel uncomfortable you can place their bowls further away from each other. little by little they will get used to the smell, then you can let them see each other but again, through a screen door or a baby gate or whatever you can get a hold of that will work inside the house, just make a trip to the thrift shop.

Another thing which i always do when I introduce rabbits together but it works the same for cats, is placing them both in a totally new territory, it can be a room in the house they have never been in or a friends house if you have someone who is willing to help, a place both of them had never been before so non of them owns the territory, which wont give them a reason to fight. then what you can do while there is play with them simultaneously with some kind of fishing poll toy or whatever they like and let them focus on the toy instead of each other, feed them treats and just let them get used to each other without the competition, If you could get a hold of a clicker (you can get one for really cheap on ebay) you can clicker train them that is an activity cats love because they get lots of treats and attention, I bought a book that is called "Cat Training in 10 Minutes" and it was really helpful and easy to do. once that happens Diva will relate Sqeeks to positive things, food, play and fun and will except her better in your house.

I would also provide both cat's with their own beds (even if you are used to them sleeping with you, that will just create more competition) their own litter boxes, their own food and water bowls, that way they can both run away to their own quiet place and have some peace and quiet instead of having to see each others face all the time, resulting in Sqeeks running outside.

Good luck and I hope this helps you