What keeps popping in my head even when I read what you just wrote is that the one time we broke up before we got back together. Its almost like I wanna see if I can do it again but at the same time I dont wanna break no contact.
Don't.
Accept that this has run its course and is over. One breakup should be the definitive end, chapter over, book finished, page turned, FIN.
Hacker, you need to sublimate and take the things you feel and transmute them.
Feeling like reaching out to her? Reminiscing on past good times? Wondering about the what ifs? Wanting to test your hypothesis's? Longing for her touch and intimacy?
Combat these urges. Redirect and remove yourself from these thoughts in the moment as best you can. Identify cognitive distortions in your thinking patterns and fight them head on. Meanwhile, exert yourself physically in a way conducive to growth and distracting your from the urge. You mention the gym which is great, but even a simple walk will suffice when you feel the need to break no contact.
Don't allow this woman to occupy your thoughts. You have better things to concern yourself with like: your well being, your finances, your future and most importantly your children. Keep the things important to you close and prioritize them and not her, never her. Work on yourself internally and with time things will get better and no contact becomes your default state.
An exercise you might want to try goes as follows.
Open a word document or grab a pen and paper. List her seemingly 'positive qualities' then sit with yourself, remove the rose tinted glasses and attack and challenge the things you jotted down. Simultaneously, make a list of her negative qualities and expand upon them as much as you can.
Be as vile, rude and angry as you wish, this document is for you and you alone. This should be cathartic while giving you a more grounded rational view of her and the relationship as a whole.
You can expand this idea as you please.
Consider journaling and letting a stream of consciousness flow out of you and vent it out. Once you've become more self assured in your ability to not break no contact you need to allow yourself to banish her from your thoughts. If she pops up, simply allow the thought to pass. Acknowledge it and make no action towards it. If you struggle with this then again sublimate, go for a walk, watch a movie, call a friend, play with your kids, get some work done, distract yourself.
It does get easier my guy and I don't consider you less of a man if you did succumb to contacting her. We are human, it happens and normally not for the best of reasons. We all have stories of breaking no contact or being contacted again, in nearly every instance the juice ain't worth the squeeze.