I see both points of view. It is unreasonable of her to come into your garden without permission, unless it is an emergency (we did this when looking for a lost child - not ours!)
It is also not something in itself to get too bothered about. However, I suspect that Carole has other reasons to be bothered about this neighbour, who has done this before. Wanting to take down a fence panel (to get into the next garden along?) may indicate distress, but my immediate thought was someone who is beginning to dement, or has some mental health problems.
Reading between the lines, it sounds as if the neighbour is fussy about her cats, but actually not that careful. Sadly, I have known quite a few people who act somewhat obsessively about their animals in this way, so I would be rather concerned. The collar suggested sounds like good idea, but I wonder if she would take notice of you? maybe another neighbour could suggest it?
The advice about a lock is also a good one, but depends on the layout of your house and garden - would be difficult for us.