If I were in your situation, I think I would still go, however buy a fridge to keep in your room to keep your food separate. I would probably prepare all meals in a seperate, clean area and then just go into the kitchen for cooking the food. I think with that many people, even if they are willing to 'try' to do everything GF, it just isn't possible to keep it 100% GF.

Or maybe you can setup a scheduled time in the kitchen to prepare GF meals and then set aside (in fridge) until it needs to be cooked. I am thinking first thing in the morning before anyone else hits the kitchen or last thing the night before - after the kitchen is cleaned.

Where there is a will, there is a way. I don't think I would expect to be included 100% in the cooking or having allowed access to the kitchen though. Not with that many people. Now that I think about it, I would probably do option number 2 above. That way I would just know that things are safe.

As for cleaning the remainder of the house, I would not put that responsibility on everyone else. You are responsible for your health, wipe things down before you sit. Maybe you can do what my son's school does - keep a handy container of Lysol wipes in every room. Easily accessible and convenient. Then, maybe, just maybe, your family members will take the initiative to clean up after themselves. (That would be a big MAYBE if they are anything like my family. )