OP, is this you?
http://www.dcurbanmom.com/nanny-forum/posts/list/327538.page
I am very sorry that you still proceeded with the extension. We could have seen this train wreck from a mile away. But I guess it's not worth belittle on this, now you need to rematch (I hope you listen to the advice this time).
All the reasons you listed are excuses. Yes, rematch will suck, but it will suck a lot less that keeping this awful, disrespectful au pair. Just put on your big girl pant and get on with it.
Switching agencies?
Register with 3 or 4 agencies if you need to. Just know that if you are with CC and APC may not issue you a refund, only a credit. Find an agency who will help you in case of rematch and won't screw you with their refund policy. Aside from $$ lost (you will definitely lose some money, especially if you prepaid for your full year- should have considered this scenario before extending...), switching agencies should be a breeze. Each agency will have their own way to put you in touch with rematch APs. Ask how they do it and speak with their transition coordinator before committing.
Telling you AP?
Call your LCC right now and let her know that you are going into rematch and she needs to prep the rematch papers ASAP. Have the conversation with AP. Should be easy at this point (if you are the same poster as above, then you did have a reset conversation last month right?). If you feel more comfortable, have your LCC with you when you have the rematch meeting.
Transition?
Well transition can be sucky, but you might be surprised with your AP. If she is smart, she might actually be on her best behavior during transitions because 1) she will be remorseful, and 2) she will need a good referral. If transition sucks, then release her of all her childcare duty and if need be, send her to the LCC. But chances are that if she is decent person, transition will be uncomfortable but ok. Consider whether or not you will allow her to use your car for personal reasons during transition. From your original message, it sounded like she was abusing your car too, correct?
Yes, transition will suck. You will need to make alternate childcare plans, or arrange to work from home/vacation days until this is resolved, but despite its suckiness, it will be a 1000x better than living another 11 months with an au pair who is blatantly disrespectful of your rules (and now has nothing to lose since she finished her first year and is assured a flight back home at no cost).
Please please, listen to us this time and rip the bandaid right NOW.