Hedge cutting - property lines and boundaries

For reference their hedge is 2.5m - 3m
My mum went over twice to the neighbours house to tell them to cut their tree because we had picked up so many apples and leaves. My mum naturally spoke in stern tone the second time which was last year because we had already told them once.
They cut the tree down and trimmed their hedge that had overgrown due to the tree towering over their hedge a couple weeks back.
However half the branches were left on our side of the garden and there were hedge branches leaning over towards our garden and over the my left neighbours fence. It was there for at least 4h so my dad asked them ‘excuse me whats gonna happen with this one’ and they said we will take it away so we said thank you.
Then she suddenly switched up like “give me the branches I don’t want you lot upset”, my dad was like no it’s okay. She asks for contact details to ask people to collect it for us. Then she starts again “I don’t want them moaning at me about it , they’ve done it for 2 years etc.” I said no it’s heavy. Her daughter comes out and tells her to leave it because she’s injured and stuff but she’s stubborn and so my dad attempts to give her one and she’s like no that’s too heavy for me.
Next morning people come to collect the branches and everything if fine. But there’s still that massive hedge branch leaning over towards our garden and over the fence.
Few days later my dad cuts the branch and a few branches that were too oddly shaped that would have grown over our side of the property. My dad said they were watching him cut them so they only came out once we were done cutting all the odd bits. A Man comes and says “this is not my house but that looks really weird”and he swore at me. Then he went away.
The woman comes and starts swearing repeatedly and speaking loudly neighbours heard everything. ‘Don’t touch my hedge’ millions of times.
Then an hour later she comes and apologised for swearing and says how stupid the hedge looks bc it’s wonky and there’s gaps in it and claimed that mum mum intimidated her daughter to cut the tree last year. The woman claimed that she herself was crying about the hedge and stuff. And then we went it to our back garden and she claims how we’ve basically cut her property etc arguing back and forth about it and points to the fence that borders our other half of the garden (we don’t know if this fence actually sits on the correct boundary line.) I said those branches were leaning over that’s why we cut them. And she said you could have come and spoken to us about it and I was like we don’t need to like by law we can cut things off it’s on our property. And she said no. It’s my hedge and stuff.
And then we started talking about property rights and why she was so bothered by about her hedge if she could easily dump her own trimmings into our garden. She said she would contact her lawyer now I am worried.