Last weekend whilst the kids were in the paddling pool playing and actually being pretty quiet tbh both of them flew to the fence and started screaming about how we were ruining their lives, she sits crying at the noise we make. We have no consideration and should be ashamed of ourselves as parents etc. They went completely nuts and I told them we did our best but they didn't believe me, hubby at this point stood up and told them to back off as our kids were watching.
Wow. They should try living next to MY neighbours.
First thing you need to do is keep a record of EVERY SINGLE ISSUE they create - what is said, when, to who and what was going on at the time.
If you can record your kids playing in their own garden etc to gaguege the sound levels and back you up then all the better - NOTE - do NOT record your neighbours. You only want an example of how your kids play normally.
If they are housing exec or association then you can complain to them about it directly. Likewise if they rent you can speak totheir landlord.
Otherwise you are going to have to deal with the police. This is where you evidence needs to be in place - so keep records.
Also, DON'T pander to them. Continue on as normally as any other family would. They moved in knowing there were kids, if they don't like it tough.
In terms of their issue with noise - unless it's before 8am or after 11pm there's very little that they can have issue with regarding general noise - this includes parties etc - so if you are, for instance, having a BBQ then it's fine noise wise.
Sound from the likes of DIY or building is usually considered reasonable until about 8pm.
Basically you rbneighbours don't have a leg to stand on and the fact that they haven't made a complaint to Environmental health suggests they know this.
But think about it - why SHOULD you keep your kids in the house in silence in glorious weather just so these two can have a quiet dinner in their garden?
Don't pander. Don't worry about the noise if it's reasonable and record everything. What they are doing is harassment and that incident where they were both at the fence is troubling - especially as it was infront of your kids and has frightened them.
Get your evidence together and get your ass down to the police station asap.