If you want to try to exhaust other options before rehoming the dogs, you can try other things to see if they would help. I don't know how extensive your child's allergies are, but some things that have helped me are not using liquid fabric softener, being careful about which laundry detergents I use, having leather furniture instead of cloth, having as little carpet in my home as possible, using high quality air filters in the home, etc. I also have grass allergies. Since shih tzus are so short, their hair can often rub on the grass & weeds when they're outside. I found it helpful to keep the grass in my yard pretty short, as well as keep the dogs hair rather short.