Cat peeing in house:-(?

Last January we adopted a female Maine Coon mix from the shelter. They stated she would not let anyone pick her up-but she was very friendly to me and to my 5 year old son. She was already fixed so we ume she was a house cat once. She was fairly aggressive from the start-she will bite me if I am near my son and he shows any sign of being upset and she has our 40 pound dog shaking in fear due to her aggression. My 14 year old cat just flat out avoids her. She has bitten my hubby twice. When she bit my son we went to the vet and after a full work up, decided she is overly attached to my son and has "claimed" him so she feel ok keeping us away and correcting his behavior. So she is now on 5 mg of Valium daily for her behavior issues and it seemed to help. Then about 4 months ago she started peeing in the house. Trip to the vet, shot of antibiotics in case it was an infection-again, likely a behavior issue. She stopped peeing for a bit but this weekend we moved things in the house a bit so we can have gas logs installed in the fireplace and she peed in the floor. We woke up this morning to find a second pee spot. My hubby has put her outside-and I am beyond upset. I can't have her destroy the house and honestly, the dog and other cat seem much calmer with her outside but I feel like an adoption failure. We live on a dead end street so very little traffic and I have gotten her a small dog house to make her a nice comfy place to sleep on the carport. I am just a bit stumped as to anything else we could have done to keep her from haivng social issues like marking. I know when I have to tell my son about this afterschool today he will be upset, but I just don't know what else we can try. We have pretty much turned the house upside down the last few months to keep her happy so she won't attack us or the other animals. Any suggestions?