It's fine to vent. It's ok to be upset. But as much for her own wellbeing as anything OP needs to acknowledge that this is about her rather than the children. Because this won't be the only thing which could cause upset. In fact the children may love this woman and may go on to form a happy healthy relationship with her, and this in itself could be upsetting to the OP.
At the moment there is just one woman. There is currently no talk of a string of women or anything like that, so for anyone to be suggesting that there is, stop projecting.
For the OP, clearly this split isn't something you wanted, and it's evident that it hurts that he has moved on and more importantly, is now looking to introduce your children into his new setup. Detaching from that is hard, especially as you're still in the grieving process for your own relationship.
But you need to put a brave face on this for your DC, and vent here, or to friends, or family or wherever is your support afterwards. But don't let the children see your discomfort at there being another woman in their dad's life. As hard as it is, she may be around for the long hall. And as difficult as it is, your children are allowed to like her, to have a relationship with her, and the more you enable that, the more your children will feel that they are not caught in the middle between the two of you.
And if your children are unhappy with the way things turn out, simply listen to them. Don't coach them, because their feelings are theirs to own, be those good or bad.
And he will make decisions which you roll your eyes at. Similarly though you may make decisions which he may be 
at. You're no longer a unit, so no longer run suggestions past the other.
My eye roll moment with my ex was when he announced just two years in that his GF was pregnant. For me it stung partly because we tried for a second baby for six years without success, a fact which he then chose to tell my DS. But on the other hand they weren't living together at that stage, but also there would be a thirteen year age gap between DS and the baby, and I couldn't imagine how DS might feel. As it was he wasn't happy. But a pregnancy is not a real baby is it, so I very much had to enable him to keep an open mind to the fact that actually, he might like this baby once it arrived. And he does.
And for those suggesting stopping contact. None of you are saying that with the interests of the children in mind either. We're talking about one introduction to a woman who may actually remain in their lives for the foreseeable future. If you honestly think that stopping children seeing their father, going through the courts, getting cafcas involved (because that is what would happen) is preferable to the children being allowed to meet daddy's new GF, then you need to take a long hard look at yourselves, and your children better hope to God that your marriages never break down - because of the damage you can inflict on them.
Views like "withhold contact" should have no place on a thread like this. Those views are not supportive of the OP either.