How can I help with this please?
I wouldn't worry about that. She can have tantrums all she wants. Cats are semi wild animals in law and free to roam.
Do you mean trellising ?
Battons just look like normal fences.
If you mean the sharp edges on the top then they are not unlawful per se but if anybody injured themselves upon them you would be liable.
If this is your fence then she should not be tampering with it.
If she does then you could sue her for the cost of putting it right.
The only thing to consider is that if you get involved in actual legal actions against neighbours you do have to disclose it when you sell the house.
The last image doesn't show much?
Does that overhang into her property?
In that case, she could remove that. If it overhangs then that is trespass and she would be entitled to use a self help remedy although she would have to return it to you.
All the best.