It is always better to keep control and keep it simple.
Write to her saying you will fix it after 7 days.
Provided you do not need her permission for access , just do it.
I would not bother to bill her for the guttering , the cost of solicitors letters will be more than her half.
You can replace her half on the basis that you are providing her with a new gutter and , as such, she is better off than before.
If the situation is left she may begin to have the same problem of damp in her garage.
OK , let her enjoy herself, perhaps at some stage she will stop to think.