What 's Mine is mine, What's yours is yours...

I have a coworker who has personal space issues.  Consistently I can be working on something and she will take it from my hands asking is it hers?  She also allows her messiness from her desk to spill over onto mine. if we are busy, working on patients, her work from other patients ends up on my desk. (Thus the snatching)  But I have put her stuff over and over back on her desk and pointed out that she needs to keep her stuff to her desk and let mine be.   Another day I had left some change and 2 dollars in a drawer in my desk that I left unlocked by accident.  The next day I came in and she starts telling me I should lock my desk since I had money there.  So I asked why she was even in my desk to begin with.  She stated she was looking for tape.  So I said ok, so go ask your lead for the keys to the supply cabinet and get some for your self, and anything else you might need.  Don’t go rummaging through my desk, I don’t like it.  I can’t seem to get it through to her that the end of her desk is the end of her area.  I am at a loss, I like the woman but at the same time there is constant loud chattering while we work and she is constantly drawing my attention away from work I am doing to work she says she needs help with or doesn’t know how to do (although she has been working at the job for at least 15 years).  I am getting frustrated and am afraid I will get angry with this person but have no clue about how to maintain a professional working relationship with her when she can’t be professional.