Well you have to give whatever notice you have stated in your contract .... Mine says two weeks. I would write a letter very short and to the point such as
Dear xxxxx

This letter is to inform you that due to ongoing behavioural issues i am terminating care for xxxx as of oct xx 2014.
Regards poppy

I would tell her in person and then hand her the letter and say this is for your records I would also wait till after she has paid her next two weeks fees unless you really don't want her two more weeks and think she will just pull but don't provide care without payment first In Other words if you give her two weeks from today but she is only paid up till Friday then make sure you get full payment for the remaining days before Monday or she doesn't get to stay