This whole situation is exhausting and will drain you emotionally and physically. Try and take care of yourself. Easier said than done. Detaching is hard. Right now the ONLY thing that matters is getting your wife back -- I get it. I was there. Hard to believe I could even function.
Not knowing what to do makes it worse. Not knowing how long your wife will remain in Limbo, chasing after other men, away from her daughters.
Your wife is acting in a way that is damaging to you and your children. I suggest you make plans to secure your daughters' safety, security and future with you. See a lawyer. Start logging evidence of any infidelity, her time with the kids, etc.
At some point Jefe, if this doesn't resolve itself soon, you will need to start listening to Starsky very closely. The "nicing" your wife back into the marriage is not sustainable for long -- you will collapse from exhaustion. Starksy saved his own marriage and has seen hundreds of people on here walk the same path you have. Trust him on this.
My hope is that one day you'll wake up and realize, "My daughters and I deserve better than this" and take steps to secure a good life and future for your family on YOUR terms WITH OR WITHOUT your wife. You may still be open to your wife returning, but instead of scrambling around trying to figure out how to be the perfect husband (trained seal act) and blaming yourself for all this mess, you'll be resolved in moving forward and living a great life regardless of what your wife does or doesn't do.
Your mindset is to remove your wife from the equation and move forward AS IF she isn't going to be in the picture. These may be slow steps, but they need to be taken to protect your girls. Your wife may not be aware of these steps. She may only sense a few of them. She will slowly get the sense that you are moving forward and she either gets on the Jefe express, or she's going to miss the boat (to mix a metaphor or two).
Right now, your wife is treating you like an option, while you are making her a priority. This dynamic is debilitating to you and unattractive to your wife. I know there's something vaguely romantic about you keeping the home-fires burning, being the rock, saving the family and being all "Christ-like" while your wife wanders off in a far country meeting men in bars, neglecting her daughters. If she's sowing her wild oats, this may be a long-haul, and there's no guarantee your wife will snap out of it while you "stand". My ex dropped the bomb in 2006 and only got worse. Her last two boyfriends were ex-cons and one of them had a drug problem. My main goal eventually was protecting myself and my children.
