I agree that you are best to simply not share things with her that you do not want her telling others.
Unless, possibly, her facebook page is set to public instead of only her friends--I am not really sure I understand how her sharing things with her friends there is all that different than if she shared over coffee, etc.
My in laws are not on facebook, but they meet up with friends every morning for coffee---on multiple occasions when visiting and out for a walk, or shopping DH or I or DD19 have run into people who recognize us and ask things like asking DD if she heard back about that scholarship yet, or DH how he likes his new boss, etc--and these are people we have no recollection of ever having met! Why? Because my in laws and their friends love nothing more than to tell one another about their kids and grandkids and all that goes on with us. Luckily for us, while we find it a bit disconcerting, we don#t really mind s we feel no need to stop sharing with them, or ask them to stop enjoying sharing with their friends -- but if it DID bother us we would just be more careful about what we told them.