If you (and your ex of course) could meet up somewhere neutral with your children and his girlfriend, maybe for a coffee, followed by a playground - or maybe vice versa would be better, when your children have managed to run off some energy - then you should be able to get at least some idea of his girlfriend, and how she interacts with your children, and obviously, how they are around her.
I'm not sure from your OP @Jmcg3011 whether your ex has ever had the children stay overnight with just him, yet? If not, I think that that needs to happen at least a couple of times whilst near you, to make sure that they don't get upset while away from you for the first time. After you have met the girlfriend and seen her with your little ones, if you still feel really uneasy about the prospect, then ask your ex that the 4 of them have a few daytime outings first, to see how things go.
One other thing, if your ex already has them overnight, or for a weekend, as long as he stays in this country with them, I don't think you can stop him from taking them away for a couple of days, either with or without his girlfriend.
Good luck in getting it all sorted out amicably 🌻