My two kids also have life-threatening allergies. I ask friends and family to not have any nuts or peanuts around when we are visiting as these are their most serious allergies. I'm OK with people eating eggs, milk, etc, which are their less serious allergies, and while I don't generally eat them, DH eats both in our house.
I think the suggestion to be the one to supply all the snacks at playdates is good - I often do this for my own peace of mind, and to make it less confusing for the other parents. . . some foods are laballed as 'may contain traces of' and others aren't labelled but actually might contain traces, etc.
For the PP who said her ILs routinely keep peanuts around when they visit, I would have a very serious conversation with them, and if they still don't change, I would not visit them anymore. It's not worth your child's life to visit people who just don't get it. I'm lucky that all our family and friends (so far) have respected our policies, except for one incident with my SIL, and I believe it caused a rift in our relationship, but I'm still glad I said what I said to her (as politely as I could, but she still took offence).
Good luck.