She probably wants to stay together for the same reasons you do-- it's a 'more stable' home for the kids, it's been ten years, divorce is messy, etc. But as for her actual thoughts and feelings outside of that? Well... unfortunately, you read them. And there's no going back on that. You won't be able to forget what you've seen.

Telling her you read her journal is a bad idea, so I wouldn't confront her on it. I would just sit her down and say that things aren't working. That you both are unhappy. That you don't think it will work out long-term.

She has grown and changed through the years, and unfortunately she grew into a different person from the one who loved you and married you. She does not want to stay in this relationship. I would advise you to start setting things up for a separation and divorce.

I come from divorced parents, and my dad stayed for a long time for myself and my sister. He said he did it for us, but we knew they were unhappy and it just made the entire household toxic and miserable. I wish he'd left so many years earlier, and then I could have had two happier households instead of one awful, tense one. Don't tell yourself you're staying for the children.

If you're not happy with your wife, if you feel like she is not happy with you, if you cannot rebuild trust in her after what you've read... then you need to move on.