I agree with all the other posters. This needs to come out in the open. littlbitlonely is spot on when she says: "They have an absolute birthright to know about each other" and "they will have a relationship that outlives your own."
My DTs have four half siblings (though I don't like the word half, as it is too often used to imply 'of lesser importance', not that I'm suggesting that's what you mean here.). The eldest is with one woman, the other three are with another. All of us are XPs of the same man (he was busy...). I get on well with both mums and my children have a great relationship with all four of their siblings, although it was understandably a bit awkward/weird in the beginning.
Try using a bit of psychology on your DP's X. Rather than using the sensible, moral argument here, can you try suggesting that not telling might hurt her badly? Get your DP to point out to her that once your baby is born, even if she, you and your DP never talk, others will. It is extremely unlikely that this little girl will not find out, probaly through the school playground, as kids often eavesdrop on their parents conversations and someones parents are bound to make a comment at some time. IT is quite likely that the little girl will then become very angry with her mother for witholding the information. Does the mum really want to run the risk of losing her child?
You may get further with this approach. At the moment, the mother probably feels a bit threatened and usurped and thinks she is protecting herself and her daughter by denying you and the baby exist. By changing the emphasis so that your DP can explain that she's actually running the risk of alienating her daughter, she might be more amenable to being open from the start.
If social services are involved, can your DP talk to them about this? I don't know the complex back history between your DP and his X, but social services would agree that the little girl at the centre of all this should know about her new sibling when he/she arrives. They may be able to broach the subject themselves in terms that your DP's X may find more agreeable.
I must stress that this is my own personal viewpoint, but taking everything you've said at face value, if I were in your situation, and I had tried every reasonable way to get the mother to agree to tell her daughter, I would go ahead and tell the little girl anyway (in a way that does not attach any blame or accusation towards her mother). This is too important for her not to know. No court in the land is going to restrict your DP's access to his daughter for telling her that she now has a sibling with his new partner. In in ideal world, your DP's DD should be coming to spend time at her dad's house anyway. Would she not wonder about you and the baby anyway? I'm assuming that there is no history of mental illness or abuse on the part of either your DP or his X. If there is, that changes things considerably, and while the goal (to let the siblings grow up knowing each other) remains the same, the best way to achieve this could be totally different.
Good luck. Hope you get it sorted.