J - There have been times where I have went out to eat with my W and times that I have not. Maybe next time tell her "no" if she asks, if that is what you truly want to do. I declined dinner with my EW on Sunday because I did not want to give my girls (they are young) the wrong impression.
I think if you tell her "no" after a few times of hearing it she will probably stop asking.
Early on my DB coach told me to plan things weekly to do together as a family. IMO if you and your soon to be EW get together once a month with the kids for dinner or to go see a movie and your children get to interact with mom and dad together IMO that is a good thing. As long as it doesn't confuse them.
My guess is once you start a serious R with someone else though this won't happen.