So my needs here are the thanksgiving thing,
Why would you want to invite her? What would be the benefit? In my opinion, just say you have dinner plans and leave it at that.

do i stay around during the lessons tonight,
Thats up to you. I kinda think that since you go to most all of them and this ones on her night, that its ok to drop them off get them going and head out.

and finally is it still too soon to start some communication with her?
To what end? What kind of communication are you suggesting? Its been, what, 2 weeks since you signed the agreement? What do you think has changed in that time?

I feel like she may the kind of person that may have some feelings change but will feel she can not approach or break the routine because she is stubborn and feels that I may be done with her and she couldnt come back.
This is totally you projecting on to her. Be patient. Keep learning. Keep growing.