Woooh there!
Yes, in future make sure that you know the address of where they are staying.
For now though you need to sort this out. Going in calling her a tart and saying she doesn't know how to look after children is only going to inflame the situation.
You need to seperate your feelings for her and him from your duty towards your children. (As does he, I might add, but he's not aksing for help on MN!)
Tell him in a reasoned way that you don't think its in the children's best interests to stay alone with someone they don't know that well yet.
Once you have them back then you need to talk to him and organise some ground rules. With the help of a cousellor if necessary?
And yes, if he and new girlfriend are living together (I assume so, seeing as she is looking after them while he is at work) then she will be looking after them to some extend when they are with him. I know it hurts, but your best bet is to ask to meet her/speak on the phone and talk to her about what you expect for the children, maybe talk about bedtimes, how to handle ADHD etc.
You need to know that you can trust her to look after them. But this can happen in the future, not necesarily now, but it has to happen at some point.
I feel that maybe he is not giving you the address as he is worried you will storm round and cause a scene. You have to act so that he knows this is not the case.
I do understand how you feel, so please don't flame me! Just wanted to give the other side of the story.
Its not being able to get to your babies, but you need to act in the way that is going to be best for them, both now and ongoing.
You got to act in a reasoned way so that you are not labelled the physco ex, which will only make things worse for the kids.
I hope it all works out ok for the kids. Keep strong.