It happens all the time, you set up a successful business and then another rep comes along and steals all your customers.
So what's an Avon girl to do?
Firstly try and work it out peacefully with the other rep. Phone her and explain that she is intruding on your territory that you have worked with those customers for some time. 8 times out of 10 she'll apologize and you won't hear from her again.
The other times you're going to have to be ruthless. Call your upline or manager and see if she can sort it out, sometimes an authority figure is enough to scare off the other rep. If that doesn't work you are going to have to explain to your customers what is going on. It's best to be upfront and truthful in this situation, if they are your loyal customers they'll stick by you.
It can be an awful situation, but don't just sit back and hope that she moves on, you need to fight for your rights.