Another option is to put up a sign at the local allergists office or talk to your Dr and Gastro to see if they can give your name out to parents. (Learn what questions to ask parents with food allergic kids, ask the allergist office if you can watch a video on TwinJect and Epi-pen or have one of them train you.) PM me if you want more info.
In my case, I have two kids with food allergies and one also has Celiacs. I would love a sitter that also had food allergies or Celiacs. Right now I only use teachers or friends that are adults. I don't use teens becasue I just don't know any. Most importantly for me is a responsible, trustworthy person, who will listen and understand the food issues that surround my kids. Personally, I have given my few sitters a choice of nights that they might be available so we could go out on a date night.
As for your concerns about watching those gluteny eating little kids

I would probably recommend avoiding the very young (like under 1 or 2 yrs old) they are usually a mess and always covered in some form of gluten. But older 2 yr olds should be fine. Discuss your allergy with the parents and explain that if they don't have any objections, you'll just feed the kids gluten-free foods that are mainstream like hot dogs and hamburgers, nachos, ice cream, jello, pudding, etc. Bring some gloves with you to handle their gluten breads. My house is mixed and we have gluten around. I don't get sick from it, so it can be done. I've watched friends kids who have no food issues and they usually understand that I can't touch or eat certain foods and my kids can't eat or touch certain foods too. It works out.
As for staying at your Dad's, just do the same thing in his area. Put up signs, talk to local mom's groups and Dr's offices, and you will start getting a following. Sometimes parents have an event on a specific date so that might be a problem, but most times they just want to go out once in a while and will happily follow your schedule!