Your dog ... who you freely admit to be nervous around other dogs and people ... got out, without your knowledge. Your tiny little nervous dog strayed for an unknown period of time and, for the most part, you don't know what he endured in that time.
You do know that a stranger tried to lift him and that he tried to defend himself, in fact was frightened enough to 'try' to bite her, although he didn't in fact bite her.
He then came home and ten minutes later you found out a little of what had happened to him. He "thought he was in trouble". He wasn't, but you did fuss and he bit your face.
You suggest that he has never done this before when you said "He really is a quiet and sweet little dog and this was massively out of character for him".
massively out of character for him
If my beloved dog bit and it was massively out of character for him the very first thing I would do is have a vet do a full physical check up, in case there was something wrong.
If the vet could find nothing physically wrong, I would then have the vet refer to a qualified behavioral expert.
It might be resolved quickly, or it might be a long haul to get to the bottom of things, but I think that's the least I could do for my companion of (say) a decade.
I see from your most recent posts that you and your husband have decided not to investigate for either possible physical or behavioral causes. You have decided that you will take him to the vet to be killed ... put down.
I understand that you are probably a bit shocked (especially when it is so "massively out of character for him") and in that shock are probably thinking that he is now going to bite your DC, but I really hope that you will decide to give him a chance ... at least by having your vet do a full physical check-up and if necessary referring on to a behavioral expert.
You say yourself he has been a quiet, sweet dog hitherto ... so for 10 years (and for those that might be thinking 'well, 10 years old is near the end anyway', chihuahuas are the longest living breed ... 18 years old is fairly common, with a lot living even longer).