Are you asking if she is able to do this?
If a tree is overhanging then I'm afraid a neighbour can cut back the offending branches.
They are not likely for the impact upon the tree overall if it does indeed overhang.
What she cannot do is cut it back beyond the boundaries though. That would be a civil criminal damage.
Sorry if that is bad news.
Can I clarify anything for you?
If the branches over hang then she can remove them.
The impact upon the tree is not her issue I'm afraid.
If that leaves an unstable tree then it is for you to resolve that although the removal of overhanging branches should not normally have that effect.
She is under a duty to return the foliage to you.
She should do that without causing damage but she must return it to you.
Yes, if she cuts back to the boundary edge.
Yes, she can cut it back to the boundaries.
Any further is criminal damage.