Find a balance that works for you. If doing things on your own was an issue from the M then it could be seen as a problem now also. BUT, not if it was because you weren't spending time with her. That ship has sailed and she doesn't want you to spend time with her anymore.
Also, stop thinking about giving her the impression that you have given up on the M. SHE ENDED THE M, THERE IS NOTHING TO GIVE UP ON. You want to get to the point where she feels you are moving on with or without her, that you accept and respect her decision to end the M. That you will be ok no matter what. Its counter-intuitive but its the mindset you need to get into. Especially if she begins dating.
If the issue was you didn't spend time with the kids, then yes spend more time with the kids. No one is saying go full GAL for yourself. Do much more GAL with the kids than you did before but add in some time for yourself also. You need to enjoy life and find something to do. If one or two nights alone seems reasonable right now, do that.
Accept what is, let go of what was, and have faith in what will be