As a parent of two boys, footballs going over the fence was a regular occurrence. I put up a net, put some padding against the fences, were not allowed to scream and shout, told them they were not to bother the neighbours by constant knocking for their lost balls and took over numerous bottles of wine as an apology. Generally they did their best not to kick the balls over and to play nicely. But if they had friends round, they were often less careful. If they’re kicking balls over, they do have to accept that the dog might get them first! That’s life, natural consequences…
I would much rather they were outside playing (in their own gardens, not in the street kicking balls against someone’s wall or whatever) compared to being inside gaming constantly. And it totally boils my piss when people say “just pop the balls and bin them”. They are children playing! Don’t buy a family sized house in an estate full of kids if you don’t want to hear child noise or deal with the odd football.
We moved eventually because my boys were continually threatened by one set of neighbours while they were playing nicely in their garden by that if the ball touched the fence (MY fence!!) they “wouldn’t be held responsible for their actions”. Kids need to learn to play respectfully but equally they need to not be too scared to play in their own garden because adults threaten them or destroy their property.
My kids are grown teens now and can go to the park with their mates to play footie now. We also moved to a house behind a playground/park and continually get balls kicked over from
kids in the park. They are all respectful and knock politely for their balls. I have zero issue with this, I let them come round the side of the house and have a look in the garden for themselves and will chuck balls back when I spot them come over. It doesn’t bother me in the slightest, I’m glad they’re out having fun. Cycle of life - pay back for all my kid’s footballs! The little girls high-pitched screaming in the park bothers me much more 😂
OP, instead of being at their beck and call with a bell - could you just have an agreement with them that they can let themselves into your garden to retrieve their own balls at certain times without bothering you? Or would this cause an issue with your dog?