i would send them a formal letter statign that next time the dogs get in you will open the gates... also state that you will be installing some sort of dog deterrent such as barbed wire on your lawn or around the holes, that may injure the dogs or something - DONT DO THIS OF COURSE - but the threat of ti may make them believe you and sort it out.
also include some literature about the dangers for kids an dog poo...and mention if the kids catch anyhting it will be on their heads...and you will sue
re the fence, you could just staple some chicken wire over and leave it at that.
i know this all might sound nasty but i think you need to fight them with like versus like...people like that are not phased by letters an courts an rights etc... if they know you will give as good as you get they may just back down... buy a set of dummy cctv cameras an install very visibly...
be prepared though