Cats have a right to roam.
Not in my garden they don't.
However, OP, everyone has, quite reasonably, gone down the cat avenue, so I will offer some other thoughts. I notice you have children, who will now be older. Are they causing noise, thumps and bangs through the wall, do they hang about or play in the street in an antisocial manner? Are there parking issues in your street? Do you have a DP who is a bit of a nob? Do you walk across her drive, put your bins out in an unthinking matter, come home late and shout at each other?
I merely ask these things because you do give the impression of being a bit, um, unobservant?
Could it be the case that there is another cause/ a number of causes for your neighbour's dissatisfaction, and the cat is just the final straw?
Time for some quiet and honest reflection maybe, try and put yourself in her shoes. If there is genuinely nothing, then it's probably the cat, but it's well worth thinking about it before speaking to her.
Otherwise, maybe she has other difficult stuff going on in her life.
Just a thought.