If I thought my 5 year old was at risk from it I would either take it up with her or put a fence down the dividing line of the properties to ensure my child couldn't stray into their side of the garden and come to harm. I'd be confident in the cat's sensibleness to avoid the barbed wire and so that to me wouldn't be an issue.
In that case the sensible thing to do is probably go to her in as pleasant and non-confrontational a way as possible with your concerns, mentioning your DS's 'special seat' in A&E. Hopefully she'd have the decency to remove it, but if not then putting up a fence would probably be a good idea. I suppose it would be possible to complain to the council citing safety concerns, it may mean they order her to remove it, it may not.