If your courts are anything like ours they're used to people lying during a divorce.
The worst part is leaving the state with the kids. I had to watch mine walk away from me at Sydney airport. I flew over with them and handed them off to my ex and her BF. That was one of the hardest things I've ever done.
But It turned out great for me. A year later almost to the day they flew back and my ex stayed in Sydney.
That was 8 years ago and all three of my kids are doing great.
Meanwhile my ex moved back to Adelaide 3 months ago and she's desperately trying to reconnect with the kids. That isn't going so well. My girls are 22 and 23 and my son is 16.
Just love your kids and be the best dad you can be. The rest doesn't matter. You can recover financially. And she'll have to live with her lies to her children about their father.