OP, I think you have our old neighbours!
We had neighbours just like this but a couple in their 50s whose children had left home and had forgotten what normal child noise was. We also have dogs and she hated dogs.
They started like yours, silly petty requests. Could we not put our recycle bin out at 7pm because they go to bed early. Having a go at DH if he got home from work at 8pm because putting his bike away disturbed them. I, like you, was way too nice and said sorry, yes, of course. The nicer I was the more unreasonable the woman got. Started going apoplectic was with rage because I started the car at 10.30pm to collect DD1 from a late work shift and told me to park in a different road if I was using the car after 8pm.
She got to the point that every day, if someone came to the door, she would come round screaming at me to stop the dog barking (dog barks at the door then stops). She told me she was getting rid of our dogs "by any means". She started swearing at the DDs as they left the house. My youngest was only about 10 at the time. The girls started getting frightened to leave the house.
At this point I contacted police for advice. They went round and put a PIN (a police information notice) on her. This doesn't apportion blame but warns the other party that the police can persue for harassment or an ASBO if the behaviour continues.
They were furious. They started putting unsigned anonymous notes through our door saying they had the misfortune to be our neighbours, everyone hates us, etc etc. they started parking across our drive, pulled the boundary fence down and threatened us with court if we didn't replace it, contacted environmental health about the dogs and phoned the council to say I was running a brothel from home (I teach piano and given that most of my pupils are 8 year olds this was so plainly vindictive). They started swearing at all my piano pupils as they arrived. They told HMRC I was earning money I wasn't declaring. None of it held water because none of it was true so none of it was taken any further but it was horrible to live with.
We kept everything documented and in the end the police said they were going to press charges. Then suddenly they put the house on the market. They told others round the estate it was "to escape some things that have happened here". I'm hoping for the sake of others they moved to a large field.
We now have amazing, lovely, normal neighbours. They make a bit of noise, they don't go to bed at 7pm, they sometimes have friends out in the garden, the house is a bit messier than it was, they tell us they never hear the dogs. I asked if they'd had a neighbour dispute declared and they said, no, the old neighbours said we were lovely! I'd love them in a way to say we are unliveable with and sue the old neighbours for every penny they have 
But the rookie mistake I made was giving in to the mad woman's ridiculous demands at the start. I should have told her to fuck off. OP, document everything and live your life as usual. Do NOT make concessions to her. Children playing and the odd dog bark is normal noise. Escalate if need be. I was a wreck by the end of all of it. It was only after they left and the stress gradually lifted that I realised how awful it had been. Don't let them change how you live your completely normal life in your own house.