You're doing fine. Make your plan and stick with it. The abundance of contradictory advice here is exactly what leads to your paralysis by analysis.
There's nothing wrong with refusing to eat together as a family. Your wife has made her intentions clear. She has come home for illegitimate reasons which you are not required to appear to endorse by sharing meals with her.
It IS possible to work towards effective co-parenting without yiedling to every direction given by a spouse who has already violated your trust by sleeping with others. And as a fellow male, I can tell you that I can COMPLETELY understand how hard it would be to do all these things that SHE is deciding need done.
Alternate meal nights with the girls is a perfect compromise. Recall that until yesterday she didn't even live in the house anymore.
You're doing well.
Blessings,
Bill
"Don't tell me the sky is the limit when there are footprints on the moon."