MM, just a few weeks ago I was in the same situation as you, just on the other side. You are legally backed up as in: your ex needs to prove he has a stable and strong relationship with that girl, minimum of 6 months. I'm really against kids being introduced to hoardes of new partners and getting confused and coming second.
Step parents are not always like this though. I really really love my dscs and they love me. They give me kisses, wave enthusiatically, hug and play with me, paint pictures and ask me for help and advice. But I also make sure I'm their friend and remind them of cards and gifts for their mummy and would never dream of taking that woman's place. When their mother's partner left her and she started the whole thing of legal action, screaming down the phone and generally turned from a normal person into Skylla over night. A lot of the lovely MN single mums have given their advice how I best deal with it and it has worked. We set up new guidelines till she feels more comfortable but I stood my ground on being with my dp all the while (I'm pregnant with our first) and also see the kids. MNs agreed it would not be in the kids best interests to 'banish' me from my rightful place at my partners side and she was being unreasonable.
I agree with you, that if your dp hasn't been seeing that girl for a long time, then maybe it's nt right to introduce them without your knowledge, but ultimately, you have to rise above it and imagine how things would be if YOU were to introduce your new man to them. Wouldn't you want your ex to be happy for you? People move on and the jealousie you feel is understandable but a waste of energy.
MF is right when she said it was immature and not well planned how you walked up to her. The girl was probably nervous and embarassed. Telling her she didn't mean anything to your ex may be the truth but how can she take you seriously??? Of course she'll laugh it off because she knows you're jealous.
Do you think mediation can help to sort out issues re childcare? It sounds as if you can say about your ex: Good riddance to bad rubbish. I hope you can learn to look forward into YOUR new future with great new experiences.
Wishing you all the best.