That poor little baby! She's been through a lot in her short life. Bless you for finally giving her a proper home. That being said, cats mark for territory! I'm guessing she feels quite insecure in her new environment. It's hard enough for a kitty to come to a home with just humans, but put a dog in the mix and other cats, it can become a nightmare. Way too much going on and it's way too stressful for the new kitty! Some cats need to be the only pet in the family.
Once a cat begins to mark, it's extremely hard to get them to stop! There are a lot of "scents" going on in your home. Your girl needs her own little territory and spot away from all the other action. Does she have her own cat tree? Does she have an area of the home where she can rest and have peace and quiet? The indoor marking seems to be a trait in multi-pet households.
Locking her away in a smaller space is not going to help! Really ... your cat is doing what comes naturally and appears to be her only defense in protecting a territory/space! Sometimes people think a cat gets along with a dog or another cat when in reality there is an issue! I'm guessing this is completely stress related to the activity going on in the home. I can tell you that my bengal loves peace and quiet. Any time the TV volume goes up or we have company and the voice levels increase, he is not happy and wants to get away (he hides under the bed). Try listening and see what is going on in your home. Watch your girl interact with the other cats. Is her tail high up in the air when she walks (not just when she marks). Or does it drag closer to the ground, which indicates no confidence in the cat.
Jackson Galaxy sells some Spirit Essences that are holistic remedies for various situations. I've never used them but some owners swear by them. The website is
http://www.spiritessences.com. Good luck and keep us informed.