AIBU to snap at neighbours who keep complaining about normal noise?

[Lilacmclovely]

We live next to a very sensitive neighbour. Unfortunately when our house was renovated for my son’s needs the council were inconsiderate regarding noise , this has now set the tone.
We know this caused alot of stress for them and we apologised but now they are taking it out on us.
They “OWN our property” therefore according to them they can do what they want in their own home. We are just council trash ( they’ve slagged us off to the whole street) we’re actually very nice people.
They complained to our council about our lift being noisy but unfortunately for them when they reported it the lift was actually broken, so y lie?
They complain about our dog who barks when someone comes home for about 8 seconds( yes we’ve counted). They complain if my teenage son plays music at….. wait for it….8pm.
They don’t seem to understand that there is give and take to living Nextdoor to someone.
We hear a lot of screaming, crying and tantrums from their garden but we just shut the door and carry on our day.
Each time they’ve had a baby we go through the controlled crying with them ( they have four children). Her husband shouts and shoots an air gun we get their deliveries for them. Their kids even threw sweets wrappers over our fence and our dog had to go to the vet! Not once have we said a thing, we’ve just ignored it.
Today I pull up with a few bags of shopping and my dog barks no more than 10 seconds and she’s screaming out of her window, swearing.
I snapped this time. I know she has anxiety, I know she’s struggling with her children but there’s a line and I’m not being bullied anymore. So I shouted back ( no swearing because she may swear in front of her children but I’m not going too) and told her to shut her kids up then.
I’m trying to be kind but I really think they have no idea how loud they actually are themselves.

You don't need to be kind, just be neutral. It's best not to shout when replying.

When she complains, state 'I could complain about your noise too.'

Advise her your noise is all normal family life, and she's fine to contact the council with concerns.

They sound nightmarish. I’m sorry. Hopefully if they have 4 kids they may need to move at some point and you’ll get better neighbours.

I had nightmare neighbours who complained about every single noise. They sat listening for it and then would put letters through my door. I used to nearly have a panic attack heading home. I eventually snapped and told them to complain and get the noise monitored and heard no more. They moved shortly after. The people who bought their house said they heard absolutely no noise from us at all.

Well I'd be reporting his air gun. .
But also block your ddg from the window if he is barking regularly..8 seconds regularly is annoying..

But that’s my point. It’s 8 seconds twice a day. Count to 8. It’s proportional isn’t it.
We have to listen to their children screaming and crying all day intermittently. We except children do this but that doesn’t help my son who’s sat revising for his exams but he gets on with it. He excepts it because he’s a reasonable human being.
I think they’re at the end of their tether sometimes and I think my dog just finished them off but that’s not my problem.

I agree with this.