Traps do work. We used to put white chocolate on them instead of cheese and it worked. The sticky mouse traps seem to work. Poison is bad, though, because they will crawl away and die. And you have to leave it where they will go which means that kids can get into it too.
Mice do carry illnesses. Their droppings are dangerous. They carry a fatal virus called hantavirus. It is a respiratory illness, though, not a stomach virus. If you do find their droppings, you should spray them with lysol or something similar, before you mess with them. Do whatever you can not to breathe in the droppings. It's actually in the urine, but they kinda come together.
Your daughter's illness is probably something else. It's the time of year when kids are going to start taking germs to school and bringing other ones home.
Total abdominal hysterectomy at age 26 due to abnormal bleeding. Kept ovaries.