I think if you had cooked or eaten the sauce and left residue on a door nob or anything else then accidental ingestion or contact reaction would happen.
if you ground up the peanuts and they were a fine powder and your child was close enough, am sure that would bring on a reaction, esp if your child is asthmatic.
worst peanuts are the dry roasted kind as they are very powdery and the dust rises in the air and settles everywere.
watching people eat peanuts is quite messy, people wipe hands on clothes and tables etc.
the cooking with peanuts means a vast amount of possible cross contamination of your kitchen , how did you clean your kitchen and reduce cross contamination?
we avoid using any wooden spoons etc as they hold residue btw.
we dont have any peanut products in our home because of the vast contamination they cause, however we do have other food allergens in the home.
we use mayo (safe for milk intol child) in squeezy bottles, and have whole eggs in the home, but avoid processed foods with egg in case son makes a mistake and eats something. we can fry and cook eggs now with not problem for our son. However this was not the case when younger as he would hive and swell up if he stood in the kitchen when I cooked eggs.
so the whole cross contamination when i cook requires a great deal of concentration and a little (huge) stress, but has to be done with the two children with different allergy problems. peanut is something that is very easy to ban from the home for us.