One time is an incident. No you should not trust the dog as if nothing had happened, but it is not enough to put the dog down. You need to reassert the rules and change the way you and the family behave with the dog so to modify the dog's behaviour.
If there is a second biting, well, you know what needs doing.
It is no easy thing to put a friend down, and I have been called a murderer by my children for putting down one of our dogs after repeat attacks.
There are no clear answers. Just do, what in your heart, is right.