
It is possible to train or dicipline a dog without violence and I agree violence doesn't teach anything, in fact it is likely to make a child think it is acceptable to hit or teach a dog that you are unpredictable or dangerous and who wants a relationship built on fear?
I was hit as a child, fortunately I decided violence was wrong but if you see the news a lot of people think its acceptable.
Positive re-inforcement, when you reward the dog for doing what you want is the better alternative. Avoid highlighting all of the negatives. You need to be the leader but you can do this respectfully, without being harsh and as leader you have privileges that the dogs don't (or the children!) What the privileges are, are for you to decide. Also as leader you must teach about dangerous situations and intervene as you feel is necessary.
I don't allow my dogs on the furniture or upstairs and this was established whilst they were new to my household. I still cuddle them, sometimes on my lap, at my invitation (I have a large GSD & a Rough Collie!) I can do whatever I like, they accept that I'm the boss.
I used to practice exclusion when the dogs were younger and doing things I did not lilke. Its like having a time out step. No harm comes of a few minutes missing out on the action! It has worked for my children and my dogs.
Good for you I hope you can educate the people around you.