He may have been chatting with her about issues in your relationship, in a similar way that we might chat to a girlfriend about our marriage and feel perfectly entitled to do so. In which case I doubt many of us would want DH looking at these conversations.
The issue here is that she’s significantly younger, he finds her attractive and yes it seems like he might have had a very minor emotional ummmm fling?! For want of better word. We all love a little ego boost but if he has an obsessive personality this ummm friendship between them needs monitoring or squashing. Personally I wouldn’t put up with it although I’m ok with very long-standing female friends of DH (who predate me 10yrs plus).
Or better yet get her number and talk to her yourself. I’ve done this before (although eons ago) and found that it really does help and the woman is usually upfront about anything that’s been going on. Then you can clear your mind, get a more informed picture, and make a plan to move forward.
I don’t think what he did constitutes cheating for most people, but it could have been the early stages of a potential affair if left unchecked. Annoyingly there’s nothing you can do about them texting now and then apart from policing his phone
.
If you both want to work on your marriage and make things better between you, things should naturally cool off between them. Be clear with him that his interactions with her (that are not work related) are inappropriate and disrespectful to you and your marriage. If he wants to vent about issues between you she is not the right person to do this with, what does she know about marriage? I’d be cross if I were you but consider your options carefully because this seems a very minor blip to consider ending things over.
Did he really get a wedding ring tattoo with your name on it!? That says it all!