I'm dumbfounded you would even consider placing your Bichons in a rescue. This is their home too isn't it? Some people suggest having the dogs meet in a neutral place such as a park works better. Have your Bichons been around other dogs much? I too, think you need to understand a little more about the pack mentality and realize these dogs might just be defending their territory. When a new dog comes in they need to learn to be submissive to the older dogs. This comes through in your attitude as well, and you should feed the older dogs first, and give them attention first. I also think the dogs would benefit from daily walking to release some of their energy. Its better to give a dog full access to the house and teach it to behave than just delegate to a few rooms and outside. We have a member here who is an animal behavioral training specialist by the name of scootiebootie, and she offers YT members discounts for special needs training. Here's her website:
LDThome, or you could PM her. Here's some tips from the Human Society
Introducing Pets to a New Dog | The Humane Society of the United States, and another one from Animal Welfare.
Dog Tip: Introducing a New Dog to a Resident Dog. I also recommend Cesar Millan books and tapes on training your dogs and establishing yourself as the pack leader.