It's certainly nerve wracking. My 4 year old has had a couple of playdates, but only after I had gone through the epipen (including using trainer) with the mother.
If the parent was over anxious about it I wouldn't feel comfortable leaving my child though. It depends on how responsive and responsible the parent was. But then, if you had any doubts about the parent being responsible you wouldn't be leaving your child there anyway.
It's upto you to educate your child and anyone caring for your child. There are so many good resources available from places like Anaphylaxis Australia (trainer epipens, dvd's etc) to help us educate and bring awareness. I make no apologies for being over paranoid with anyone looking after my child- I need to know he will be safe. If I have any doubts, I don't take the risk.
I began educating my child as soon as he was old enough to comprehend it. I am confident that he wouldn't eat anything he didn't know was safe. I have seen him reject lollies and chips offered to him from other children telling him that they were safe for him. I always pack any food and drink he may want.
It also depends on how sensitive your child is eg airborne anaphylaxis. The more sensitive the greater risk obviously. It's so hard to let go, but as I am learning it's little steps to trusting they are safe away from us.
Hope this helps a little. My DS starts school next year - still allergic to all nuts, eggs, wheat, dairy etc... I am freaking
believe me I will be seeking any help and support from this forum then! Good Luck and listen to your gut instinct