I had a friend who was in a situation very similar. It did not go well for my friend. The girl was chatting with someone all the time and the other guy was complimenting her in same manner. My friend confronted her, and she said you have trust issues (better arguments), and he apologized and was genuinely sorry.
Anyway, as soon as he was away for work for some time (other city), she was in a relationship with another guy. My friend nearly committed suicide. He was a total wreck. He really really loved her.
Its absolutely clear she is dishonest, and you love her. I am in a relationship problem of my own, and I don't know where life went wrong for me. So I doubt my own advice, but I would suggest considering that to some extent your marriage is already over because you did not find the right girl.
Can you change her - that is a good question. 26 is not teenage, your girl should already be mature and understand what cheating means. If she does not, can you jolt her out into the real world? Maybe. I am changing my life, I am trying to be better, I am trying to grow a spine, I've been really bad in my own relationship. BUT (and its a big but), I did not start to change till my SO changed herself. She took everything that I gave to her, and today she has stopped taking it, and it jolted me out. I don't think I would have understood things if she had not grown a spine first. In a relationship we all seem to play a game. We try to make our place, unknowingly sometimes at the cost of other person's place - as long as the other person allows us. Then we settle down (kind of). That is not how it should be. You are allowing your space to shrink, and her space to grow.
You have to take her challenge. Tell her that she is being dishonest. Tell her to name someone (anyone) who will understand what she is doing - and if it is the right thing. Tell her that you will have to walk out, unless she stops chatting with this other person. And if she is anything like the other girl (my friends wife), she will not stop chatting with him, and will be OK with you leaving. If you are anything like my friend you will feel sorry for yourself and then you will come back to her, and her space will grow.
I really hope you are not like my friend. If she is OK with you not being part of her life, and if she finds chatting with someone more important than being with you - you know she does not care about you. If she is ready to give more importance to your relationship she will back down, and maybe things will work out for you.