Well, obviously, as @
Bill3 points out, the content of these texts is critical. What was that all about?
That said, having been cheated upon by both of my long-term partners, what I have learned is that my gut is almost always right. I may not have had all the details, but I had enough to know something major was wrong. If you talk to lots of people who have been through this, most of them say essentially the same thing: when you know, you know.
I am certainly not saying that your husband is cheating on you , please understand. What I am saying is that you definitely have a voice inside, a sense, an intuition, a gut. I strongly recommend that you follow that sense, wherever it leads you. It is your friend. It is zillions of years of evolution all coming together to say==
danger!
This texting represents a lack of respect for you and for the marriage. It has been my experience that secret texting with members of the opposite sex (if straight) is a bad sign. If it's just that, that's still a problem in my view, but it's not a disaster, necessarily (depending on what's in the texts). If there's sexting, huge problem. But seemingly innocent texting can lead to eventual hooking up. And that, of course, is a disaster.
Personally. I would not stand for him not unfriending her. When I last went through this, I insisted she cut off all contact. She didn't, and that was ultimately that.
My heart aches for you and your kids. If he wants a divorce, he should man-up and tell you that. But maintaining a window of contact with a woman he was secretly texting with when you have expressly asked him to close it is, to me, unacceptable. I will be praying for you and your children tonight. Best of luck.