Welcome and sorry you are here. But you have come to the right place.
First and foremost, you are calling it a MLC. We all make similar or the same mistake. We think if we can define it, then we can fix it. So the first lesson for you is STOP TRYING TO FIX IT. You can't. It takes two to make a marriage but only one to D. The reality is that no matter what you want, say or do, if she wants a D you will end up D'd.
Your W is wayward. This is why when you distance yourself she stops the behavior. She wants the security she gets from you as a H AND she wants to do whatever she wants as a "separated" woman. I quote that because that is her excuse to do what she wants. But she expects you to provide your paycheck, take care of the kids when she needs it, etc. WAYWARD.
Learn from the pursuit distant dynamic (there is a thread here on that). You distance, her behavior "improves". I quoted that because it doesn't really, she just changes it to manipulate you. Okay, here is a hard fact: she has probably physically cheated on you, multiple times. Sorry to be blunt, but you need to go into this with your eyes wide open. Guys that are out for one thing do not stick around long if they aren't getting that one thing. Guys can flirt with anyone, they continue to flirt with those that it bears fruit with.
Here are actions you need to take: First, kick her out of the marital bedroom. "Where am I going to sleep?" SHE figures that out, just put her out. Ws that cheat do not get to share the MBR with their Hs. Second continue to detach. (Read what loving detachment means in the detachment thread.) She wants time and space, give it to her. Next, you admit that you aren't perfect. Make and honest assessment of your flaws and then 180 on them. This is a time for self-exploration and discovery, and a chance to fix yourself. You can't fix her. You can' fix the MR. But you can FIX YOU! So do it.
And then the most important: GAL. Like a madman. Every minute you aren't at work, or spending time with your kids, you are BUSY BUSY BUSY. Also, do new things. Make new (MALE) friends. Become the man only a fool would leave!
One simple truth you need to keep in mind. It saved me in my own sitch: You can only control one person in this world. That person is you! Stop trying to control her. Looking at her phone IS trying to control her. LET HER GO TO GET HER BACK!
Finally, employ all of sandi's rules. You can't fix the marriage, but taking these actions and following sandi's rules, being true to good DB principles, will give you a chance at a MR 2.0 with her. (Note, I realize you never said the two of you were married. I am using terminology as if you were. Sorry, but whether you've formalized you marriage or not legally, you have been living as husband and wife for years, and have 3 kids. So I still see this as no different than if you were married legally.)
M(51), W(52),D(16) M-20, T-23 Bomb Drop - Dec.23, 2017 Ring and Piecing since March 2018