Join Date: Mar 2010
Location: Ontario, Canada
It can often take a long time to introduce two cats, especially when one or more are past the kitten stage. When I adopted my two, they were both kittens and it still took 3 months before I could leave them alone together in the same room. That's not to say it will take you 3 months, just that the time required will vary with the cat.
A few points. First, has Webley now been neutered? If not, that would be a good first step. Second, I'm not sure who told you to introduce the cats first (rather than the dogs), but cat-to-dog introductions are often much easier than cat-to-cat introductions, provided the dogs are well trained and are used to being around cats (as yours presumably are). So, you might start with the dogs. If you can successfully introduce them, it would avoid the need to constantly lock up the dogs or put them outside when you're trying to deal with the cats. I wish you the best of luck!
As for the cats, whenever members here face a difficult introduction between two cats (meaning longer than a month) they usually use baby gates or the equivalent. What that means is keeping Webley in a safe room and putting baby gates on the entrance, so the cats can see/smell each other and interract a bit, but in a non-threatening way, since neither cat can get to the other. You will need to stack several gates on top of the other to cover the entire entrance (so the cats can't climb over), or use something similar that will allow the cats to interact without physically being together (I used screens). If you use gates, then one of the gates needs to be affixed so it can open (so you can get in and out!).
Have all "good things" happen on either side of the gate (feeding, all treats, all play time, cat grass, catnip and anything else the cats enjoy). So, the cats start to learn that good things only happen when they're in each others company. Continue to exchange rooms once a day for about a half hour to an hour, but don't let the cats be together in the same room until they seem to be interacting well on either side of the gate/screen. Once they seem ok on either side of the gate, you can then put them together for short, supervised sessions, increasing the length of those sessions over time.