Cornish Rex peeing on carpet?

I adopted 2 Cornish Rex cats in January 2010. Ziggy 9 yrs. oldand Queenie 11 yrs. old.They came from a loving home.The woman had to give them up because her grandchildren were having asma attacks when around the cats.We also have a Min Pin small dog Happy 14 yrs. old. We also adopted him 4 yrs. ago from the Humane Society.Everything was going well until in the spring Ziggy peed on our bed. So we just would not let him in the bedroom anymore. Then during the summer of 2010 Ziggy started peeing on the wall to wall carpet in the main part of our house.I do love having them. I would like to know what the reasone may be for this behavior and what I could do to solve the problem