My dog is not allowed out of the garden unless on a leash. This is normal to me and, I think, the vast majority of dog owners. Most people take great pains to ensure that their dogs are not nuisances.
Your neighbour sounds to be very inconsiderate to say the least.
Pepper would, probably keep them off your lawn, but a small delegation of pleasant neighbours would also be a good start. Failing that, your local Parish Council would be reasonable and try to explain the problems being caused, with a little more weight behind them.