
Like Jo I have flatcoats and yes they are boisterous, I have to keep them fit as they are working dogs, free running is excellent for them. So can see both sides of this situation. I always try to avoid times when I think people with young children might be walking around. if I spot people with small children then yes, I do put mine on a lead. I find it equally annoying when dogs just run up to my dogs and the owner says "It's alright they are only playing", when it is quite obvious that their dog has run up with hackles raised and tail erect!
There are two things you must consider, and one is, that puppies when teething are going to nip and chew, which is perfectly normal behaviour for them, how will your child cope with this? Also how will you & your wife cope with it?
The second thing to consider is that if your wife reacted by "screaming" at the idiot owner, she has reinforced your daughters fear, perhaps a more laid back approach in front of your daughter might help her get over her fear. I am not saying nothing should have been said, but I would have made my point quietly and firmly to the dog owner.
I do think that the sooner you go and see Sierra or a Pat Dog the better, and I hope your daughter will get over her fright soon.