If it isn't too late, I would not be there when she arrives. Let her wonder what you are doing.
Also, it seems to me that you are sharing the cat when you should be sharing the car. Why not tell her that you are unable to do many of things you need to do, like finding a car, when you don't have one. Let her know that you would like to set up a couple of times a week to be able to use it until you find a new one. That is a very reasonable request and there is no reason she shouldn't be willing to do it.
M 46 H 44 D 12 S 8 M 9 T 11 BD 2/15/13 "Makes sense to stay together" 5/12/13 Agree we are 'healing' 7/13 Definitely Piecing 9/13