If you filed to "improve things" then it was for the wrong reasons. Now your wife will need to show you that she wants to stay married to you to stop this. She may need guidance.
If you simply state a few boundries such as:
1. Monogamy in marriage 2. well, you get the idea
and discuss this with her then you'll get a good feel if she wants to work on this. Sure she's friendly. If she's friendly it may be because she doesn't want you to rock the boat. After all, the status quo has been perfect for her for years.
Be strong, Luke. Keep a close eye on the kids and it's up to you to decide what would be necessary to turn this around now. If the divorce goes through she may hit rock bottom she may not, who knows. Your focus should be on you and the kids. Once upon a time she loved you, she may again, but don't wait around for it. She'll let you know so don't ask, or have relationship talks (other than maybe 1 boundry talk to show her what she needs to do, such as marriage counseling (but don't say you'll stop the divorce for that, marriage counseling can also occur AFTER a divorce)).
Good luck and gods speed, Luke. My best prayers and wishes for you and your kids. May your wife see the light but don't get your hopes up.