Instead of discussing it, I would call a lawyer and ask him or her to draft a letter telling this woman exactly what her rights are in regards to branches overhanging her property. The letter should specify exactly what she CANNOT do to your trees as well. The lawyer should tell her that if she has her lawn guy or anyone else cut down your tree or harm it in any way, she will have to pay for a tree of comparable size to be brought onto your property and planted to take the place of the one that she illegally removes.
Trees up the value of your property. You know that, right? You lowered the value of your property by removing the tree you already removed. (It's your call to do that. It isn't HER call to do that.) The lawyer also needs to point out the property value issue.
The reason I'm saying to do this instead of just telling her no, is that she sounds like she will just go ahead and do it anyway if you say no. $75 is not very much for her to get her way. She thinks you took out the other tree because she pushed for it. So she thinks she can bully you into this.
Another thing to tell you (Fanged Bunny made me think of it) is that some trees can only be pruned during the winter months because of the sap that runs and bugs getting into the wounds and damaging the tree. You had better do research on this tree to find out when it can be safely pruned and tell the lawyer THAT. He or she should clearly state that if she causes the tree damage down the line because of improper pruning or improper timing of the pruning, that the tree will have to be replaced.
Please don't let her get away with it. See the lawyer. I really believe that letter is money well spent.
Dawn