I haven't chimed in your sitch in a bit but one thing comes up pretty frequently, you respond to every single one of her texts (ok, 98.9% of her texts LOL)
There is no perfect rule for this but I would say it's ok to let her wait.
If its not about the kids and some sort of drastic emergency, seriously why do you need to respond. You keep saying it yourself, most of these texts she could answer herself if she put effort into it.
Sit her down one day and just be straight with her, "look this whole process we're going through is because you weren't happy with us or specifically with me. I just didn't do it for you anymore, and you really didn't enjoy being married to me. Looking back I can see you felt like this for quite some time, its the reason why you had that first affair and it's the reason why we split up this time. I get it and I'm fine with it, and it's time for both of us to move on, I won't be knocking down your door begging you to take me back because it's not what I want anymore, truth be told I don't know what I want but I wasn't happy back there either, it's time for both of us to accept this break from each other and explore our options and see what life has in store for us. We're going to have to communicate and be civil with regards to the kids, I know I will do my part in that, but as far as all of this other stuff, maybe it's time you tried taking care of this stuff by yourself instead of always relying on me to do it, not being mean or punitive but I'm a busy guy too and between the kids, my work and my personal life, there isn't a lot of time left over to be available as much as I am to you, I hope you can respect me enough to give me my space now that we're no longer together."
It will take a minute to say this and she'll get the point.
You can be as nice as you want but I think your first D hearing is in a day or so, being nice, patient, caring, humble, helpful really isn't doing anything to motivate her to stop the D filing. I think you've been as patient as anyone can expect to be in this situation bro. You handled the first separation and her affair like a champ but she strayed again even if there wasn't an affair this time, it's like she's been planning to do this again to you for quite some time.
Detaching is really letting go. You can love her, you can dedicate a portion of your heart to her and love her enough to set her free, if that's what she wants, give it to her.
As for you, I think if you want to go out and see that woman, I say go for it. I will warn you that this woman sounds like she's in a very vulnerable position in her life, it wouldn't take much to take advantage of this situation, you have to gauge your actions, exercise your self control and do what you think you can. If you don't think you can exercise that control then you have to decide if you're calling it quits on your marriage and if you are, don't feel guilty considering what you've been through and the fact that your wife has filed for divorce, you are technically single, only you can decide when you're ready to be "single" again.
For what it's worth, you're doing awesome, you're handling this like a champ, my expectations were pretty high when I first started talking to you but I'm a pretty good judge of character, I knew you were up to the task, I knew you could handle it.