In the eyes of the law your dog is off lead and therefore NOT under control. If there is a problem no matter how capable your child is, you would be held completely responsible for an incident with an on lead dog. Not your child, and not the other owner no matter what their dogs reaction was because if their dog is on lead under the control of an adult, then you would be responsible. Right or wrong that is the law. Therefore unless you can guarantee 100% when your child is walking your dog that he will not come into contact with any other dog walkers then I wouldn't risk it.

Your choice but in this day and age not something I'd do.

Alongside my own pack of dogs I generally have 2 or 3 extra foster dogs along for the ride, these dogs have come from back grounds I have no idea about and been subjected to god only knows what and I too would avoided your child like the plague and if came across him I would most likely have been as concerned as the woman. She has every right to be worried about her own dogs actions having only owned it for a short period and personally I think her actions were extreamly responsible. Lets face it we all jump up and complain about those idiots who let off lead dogs run up to our dog aggressive on lead dogs now don't we?

Maybe she didn't express herself in the right manner but give the poor woman a break and see both sides of the coin.