How do you handle abrasive and intrusive people?

There's this woman at work who is very loud, abrasive, and intrusive... she always wants to be involved in every conversation...she's very loud. She walks into your office even though you close it (meaning do not disturb)... if she needs your help she'll sit there until your available even if your busy on a phone call or on a private conversation.

I co-run a department temporarily at the company until a new boss is hired so technically she works for my coworker and I. There was one day where I had a day off and I was checking emails at home and I replied to one she sent and later that day she forwarded him the email telling him that I was working at home. (WHAT WAS THE POINT IT THAT?)

Then recently there was a problem client who didn't like our customer service...when it was more the clients problem of not responding to our emails/calls in a reasonable the client decided to use the services at one of our other locations...this employee works at that other location...and ended up having an appt. with that client...i guess the client ratted on me to the employee and the employee AGAIN emailed my coworker...basically ratting me out...and whatever story the employee was told or if she was lying to my coworker it makes me look like I'm not doing my job

so how do I handle this situation because my coworker is a pushover...and is a "nice guy" and we also have to be Politically Correct when it comes to HR situations...