Obviously you don't want to fall out with your neighbours, but this sounds like hell on earth. I'd try making a few more friendly complaints to the neighbours before taking it further (i.e. complaining to their landlord and/or recording the noise and taking it to your local council).
The thing is, if they have two small children and a yappy dog, then surely the noise they have to live with must be loads more than you're having to put up with. Which makes me think that chances are they are pretty much on edge with the situation and might just flip if you get too hissy with them. So maybe take a deep breath, count to 10, etc, before knocking on the door. And if they flare up and tell you to F-off, try not to get angry but keep on making your point quietly but firmly. These things can escalate horribly.