oh god. turn taking.
I'm having some sort of PTSD flashback trauma 
I went through this with both of mine.
We did loads and loads and loads of work on turn taking. I bought a selection of toys that were perfect for turntaking. Like dropping a ball down a winding slide, sending little cars down a chute. Their home visiting teacher had a pig that you put tokens into and it grunted 
they had 3 sessions a week with the home visiting teacher for about 3 years. Plus I did the same work with them.
It can be a long hard slog but it can be done.
That said, I don't think you can force sharing. You have to train them to know how to share and to know that it's ok to share, it's safe (and there's something in it for them
), iyswim. Just snatching stuff off them and saying you've GOT to just isn't going to work.
Plus - do they HAVE to share? If someone came to me and asked to borrow something and I didn't want to lend it - would I have to? Should I be made to? At what point do we respect the right of a person to just say no?
Is she able to tell you what it is about letting people use her things that frightens her? If you can find out what it is, then you will be in a better position to think of something that would help her to not have that fear.
Bribery? if you let us borrow your cookery book, you can help make cakes / decorate the cakes / have some cake ?
The flip side, of course, is to make them understand that other people don't have to share with them either. This was a big problem for mine. They didn't want to share, but they wanted other people to give them whatever they wanted. It took a long time to sort that out! - if I'm being honest, we're still not there yet. "You don't want to share X / remember when soandso wanted to borrow your X and you said no? well, you can't refuse to share but expect people to share with you" is a very complicated thing to get across to a child with limited receptive language skills!
I am waffling.
sorry.