Don't feel silly, everyone does it. You are suppose to look for positive changes, it lets you know you are on the right track.
Also I do not think you slipped up on the invite. I think understand what you are saying, you do not want to be too available which is good. The thing is that she knows you are available, you have nothing going on. If you would have refused she may just taken that as you being mean.
Just try and be cool about it and maybe later when you start going out with your friends or whatever you just may have plan’s on that day so it is ok to take a rain check.
What ever you do don’t act like an excited puppy dog waiting to go for a ride…
Sucks we have to play this stupid game. We should be relaxing and enjoying our kids instead of going through this crap. The sooner you drop that rope (let her go) and GAL the better.