unfortunately with an allergy this severe (merely speaking to someone who had eaten nuts) its pretty impossible to guarantee no contact at all in a place like a hotel - the place is full of staff , and also strangers who are not only unaware of your problem and request, they are not obliged to follow it.
if its so bad all it would take is a guest to have eaten a peanut butter sandwich then touch a door handle with some on his hands, then the next person to open the door also has some on his hands and spread it etc etc
all the hotel can possibly do is ensure none of the food has peanuts in - and i dont believe a waiter would knowingly lie to someone with a life threatening allergy just to get him to eat a canape - why would he? he only said what he believed to be the case - but the waiter himself or the chef - or any staff, could have eaten peanuts earlier and not washed their hands properly.
who knows how it happened - and without a sample of the canape you cannot prove the hotel was negligent.
did the child not have an epi pen with him?
you could ask for a refund, and they may give it as a good will gesture.