A few more thoughts....
1) I recommend reading NOT "Just Friends" by Shirley Glass. She talks very clearly about 'emotional As' ('EAs'), non-physical As. Your W may not have met her ap, but she is surely in an A.
2) If an M is a power struggle, it's an M that is in a lot of pain between people in a lot of pain. Focus on using your power over yourself rather than power in your M. If you focus on your own wants and needs and focus on not letting your W control your decision-making, you'll be OK.
For example, it's one thing to know you very definitely want to rebuild your M. What you want, however, is different from what you do. It's good, for you, to know that you want R but won't actually commit to R unless your W shuts her ap down. R is simply not worth it unless the WS changes from cheater to good partner, and your best bet is to find the power within you to kick her out if she isn't willing to make that change, no matter how much you want to R.
Power over yourself counts. Power over your W? Not so much.
3) When R is on the table, I'm not big on exposing an A. Exposure can shame a person back into the M, and R works best if the WS chooses freely to enter R, IMO.
4) I'm very much against being decisive for the sake f looking strong. It's much more important to BE strong than to LOOK strong.
IOW, my reco is to file for D only if you want to D. My reco is very much not to file as a tactic you hope will get your W's head out into the open air. If your W needs to be manipulated into R, how will you know if she's really committed to anything but covering her own ass?
If you want D - for example, if your W won't meet your requirements for R fast enough for you - by all means file. If that happens to wake your W up enough to start meeting those requirements, by all means feel free to reconsider what you're doing.
Again, if your W needs to be manipulated into R, she's a bad bet. Live your life with honesty and integrity. Think straight; talk straight; act straight. ('Straight' meaning 'not crooked'.) Be yourself. Have faith in yourself. Use your power to act in your own best interests.
Young kids benefit from good parenting. They benefit from living in an intact household. I see my 12 year old GS suffering from his parents' D. But he (and my son and my XDIL) suffered even more when they all lived together. Your case may or may not be different from my son's.
Kids are an added big complication - but they are only one consideration out of several that you have to navigate. Some people stay for the kids, and it works. Some people stay for the kids, and it doesn't work.
You have to make your own decisions.
My reco is to develop your requirements for R. Lay them out for your W. If she agrees to meet them, R can start. If she doesn't agree, D can start.
My reqs were pretty common:
Honesty - no more lies
IC for W, with a goal of changing from cheater to good partner
IC for me for support in processing the anger, grief, fear, shame, and trauma that come with being betrayed.
MC - because we found a great MC who held W's feet to the fire and who dealt with the A first and kept dealing with the A until we were done with it
W had to treat me better than she treated ow.
The responses you report - sleeping, eating, despair, etc. - are all normal. Know that you can heal, survive, and thrive whether you R or D. Have faith in yourself. Your life will almost definitely get better, and it WILL get better when you find and exercise your power to act in your best interests.