Well, my husband was doing on line dating and had a long time EA with an old ex gf (long before we met) who is very long distance. He would send her gifts that were nicer than he got me and say things to her (text messages I read) that he never said to me. I had somewhat different reactions - I kind of find out about both things at the same time. I found out about the online dating when I was trying to fix his computer one night as a surprise. I got the surprise. He left screens up and there was one after another. I hit the roof and raised hell with him. He was scared and contrite and promised not to do it again - and I don't think he has. I checked for a while and never found anything else, and he never met any of these women anyway. I don't think he sent any money either. It was all fantasy for him, I think to relieve his fairly miserable reality at that point of caring for a severely demented father.
I don't think he's gone back to any of that, and it ultimately didn't bother me as much as the EA, because that was a real relationship, although LDR, with a real person and he was sending gifts and such. Not a lot of money but much better at that time than he would give me. I didn't say anything to him about that, I just kept reading the messages to see where it was going. It didn't seem to be going anywhere and his behavior towards me improved anyway so I stopped giving a shit and stopped monitoring. It took a couple of years or so to get to that point but I did. I've asked him about this person a couple of times and he tells the basic truth but not his attachment to her but as long as I don't think it affects me, I don't really care. I did lose all romantic and sexual interest in him from these experiences and have no desire to get them back. He doesn't seem to care so that's okay. I'm fond of him and love him as a friend, and I'm stuck anyway because of financial and health reasons, but I don't see any point in digging or bringing it up. We're both old and this is as good as it gets for both of us, I think. I mostly kick myself for doing or not doing various things when I was younger, with him or without him. I take responsibility for this, but not blame because I had a very bad start in life and it was enough just to get out of the poverty and abuse I was raised in, but I made a lot of wrong decisions - or I could have made better - so I take responsibility for those but I think I did the best I could at the time. Mea culpa, mea culpa, mea maxima culpa.
So, sorry to be long winded but there were NO SIGNS of any of this before I found out accidentally on the computer and phone. I was shocked, I really was, it seemed so out of keeping with him, but I guess he developed an alternate persona for this kind of thing and my guess is that's what your wife did. Developed an alternate persona, if that makes sense, to keep her A life and her married life, separate. So she's one person when she's out on the street, and another at home. This is more common than we realize. People develop alternate personas sometimes. Someone who does this, I don't know if you can spot it except by evidence you come across, which is being the dreaded Marriage Police.
At some point, if you decide you want to be with someone, for whatever reason, it comes down to whether you are willing to trust them again and if you want to keep investigating. I decided it was worth it to me to trust him again, and to stop investigating - that doesn't mean there aren't triggers occasionally, that's inevitable, but that was my decision. If I had money and better health, I probably would have left back then, so there's that. There are "practical" factors at times and I never fault people for having them. We can't all just stomp off and leave - or we could but it might be worse.
Because most of it was fantasy and not actionable, and I'm not really in love with him anymore, I don't really care. I'd care if he was planning to dump me or do something behind my back financially or otherwise, but if he has his little secrets, I can't bother being the Marriage Police to root them out. It's not how I want to spend my time. But that's how I took charge of my own life situation such as it is - we all have to take charge of our lives as much as we can and be active about what we want, what we will or will not put up with, what the consequences might be, what the boundaries are, etc. If you don't have any obvious signs of bad behavior, you have to decide what YOU WANT and how you want to live and if this person makes you happy now or you're reasonably content, because if you are....maybe that's as good as it gets.....and if you're not, you have to make changes.
I always advise people to take what action they can in their lives instead of waiting for the other person to do things and letting the shoe drop and then finding out about it and reacting. Set up your boundaries, what you want, don't want, will not accept, in your relationships and when you see it going awry - confront. Remember, the ultimate action you can always take is divorce - be sure you understand everything about divorce in your area, scope out a good lawyer you might use, and consider that you can always pull the plug if you want to. You have to be the one to assess what you want and what is acceptable or not to you, and that has to be based on her behavior. Unless you want to spend your life digging and checking and being the Marriage Police.