Can I stop my ex from moving out of the country with our two small children?

I am the non custodial parent, and my ex lives in Utah, and I in Ohio. I have a full time stable job and earn decent money. My ex does not work, and never did during marriage. Within the last month, she has met an Australian who she now wants to marry and move to Australia with. My kids are 3 and 1. What are my rights as a father, and is there any hope for me in keeping the kids and essentially her in the states? Or is it a waste of time and money, cause the courts will just side with mom and allow her to leave with the kids?