I agree with Tink. Accept the invitation to dinner but know your boundries before you go there. Texting during dinner or a movie is rude and you should not put up with it. I would ask her to stop and if she doesn't I would tell her dinner was nice but I see you have more important things to do and that you have other things to do also, say thank you and leave.
If she gets mad so be it but atleast she will know that you were serious and do not like being ignored or taken for granted.
As for a different type of relationship, this is exactly what you want. Why go back to the old one that did not work. New is better and hopfully will work.
