for anyone who thinks that meeting the new gf will be damaging etc, ought to think about what dictating when and where and how and if the children's father can see them will do to the children.
Because if the op were to withhold contact and the ex were to end up walking away as a result, the op would be partly responsible for that.
At the end of the day, never do anything that your children can ever hold against you in future, and withholding/dictating contact on your terms is one of those IMO.
It's not unreasonable to wonder about the woman who will be spending time with your children. However once you are separated, the reality is that your children will be spending time with their father without your supervision,and vice versa. And as much as he doesn't and shouldn't have the right to dictate who you spend time with, neither should you have the right to do the same with him, regardless of how soon it appears to be since the split.
From my own perspective it was my ex who engineered a meeting between my ds and my bf of a few weeks who I had no inclination to introduce my ds to at the time as felt it was too soon, then gave me an ultimatum that either I tell ds about him or he would, so left me no choice.
Then my ds met his gf several months before I did (which I didn't have an issue with) but then chose the time for us to meet at ds' birthday party.
I actually thought she was nice at the time, but my xh has since informed me what she thinks of me.
even though she was nice to my face, so I now have reservations.
But she is with my xh and as such I have no control over that.