Can I ask what the layout of the wood and the properties is? Do you have two back gardens next to each other that both front on to the wood, with equal frontages on to it? Is that where the 50-50 split (and 50-50 contribution to buying it) came from?
If so, I'd very carefully mark a boundary with stakes that finished at the end of your joint garden fence and start working on my half, avoiding the last few metres near the stakes for now in case that line gets resurveyed and moved before it's all resolved. Create a fact on the ground.
AFAIK the obvious way for a court to resolve this dispute if it gets that far is to split the wood along that halfway line, which is what you want and what you have a witness to her agreeing to. This way you can get on with your life and treat this as a loose end that just needs to be sorted before either property is sold.
The idea of starting with safety-motivated work is very good btw, as again it will be hard for her to argue against you doing work to minimise your joint liability to wandering members of the public.
You want to try to get to the point where an honest sollicitor will be telling her to stop wasting her money as she'd have no chance of changing what's actually happening in the wood, in court.