International Travel
What are the ages of your children? I went through this last year and leaving the country is TOTALLY different than leaving the state (although from your last post, CLEARLY you are not allowed to leave the state either).
If you children do not have passports (and I believe are under 14), you CANNOT obtain passports for them without consent from the mother, so you'd first have to petition the court to force the mom to sign consent for the passports (I was taken to court for this last year). In my case, my ex wanted to take our daughter to Jamaica which is a country which is not party to the Hague Convention (an international treaty which recognizes custody laws of another nation - that's a vague definition). Since his wife is Jamacian and has strong family ties there, if they had decided not to return, we would not have been able to get local government cooperation in order to ensure our daughter was returned.
If there is a real good reason for travel to Europe, you may be able to get a judge to allow it and order mom to sign the passport consent (they might require you post a large bond), but if it's just for leisure ski trip or something like that, then there is a good chance that the judge will say no. It's just not worth the risk.
I did a TON of research on this last year when I was faced with it, and what I did find is that judges have a very wide range of descretion on this issue and if you make a good argument, you have some chance of having this granted, but the worse the relationship is with you and the ex, the less likely you'll be to have it granted because the reality is that it's those type of situations where kids are most likely to NOT be returned and even if you know that you're returning, the judge can't know that and so there is NO benefit to them to take the chance of having that on their conscious. It's just easier to say no, which is what happened in my case, sort of. Basically, the court stalled the case for weeks, then said, "well, we don't have time for a full hearing, so I can't allow it".