OP - you are being far too accommodating - that's part of the problem.
You have every right to engage in activities with reasonable acceptable noise levels between the hours of 7am and 11pm - every day - weekend or not.
as long as noise levels are not excessive or mindblowingly repetitive:
Children playing in a garden would be considered acceptable.
Dogs barking now and again would be considered acceptable.
Entering/leaving premises as and when necessary would be considered acceptable.
Living your lives within your own home would be considered acceptable.
I would send the letter you posted on this thread.
I would discontinue altering my family life for anyone.
I would ensure my kids understand that they can make as much noise as they like as long as it's what is usually acceptable during play and every day life. Obviously, excessive screaming etc is not acceptable but I'm guessing your kids know this.
I would keep a diary of every interaction with this odious couple. And I mean keep a diary - every comment, complaint, harassment etc.
I would also have a BBQ every Saturday from now until end of September and each week I'd invite different friends to enjoy the garden and jubilations with.
Every Saturday afternoon I would blast my music and dance around with the kids
Every Sunday morning, I'd have breakfast outside, weather permitting.
And I would ignore everything they say or do - apart from the diary. Once you have a nice full list of outrageous, bullying behaviour, I would engage a solicitor and have them draft a formal letter threatening further legal action unless things change. I would also mention that if they every remove or touch any of your property ever again without your prior permission, you will take legal action.
Oh, and the Saturday BBQs - I'd invite them every time