Zayna, I really feel for you. It's not right that you are being kept a "dirty" secret, nor does the "truth" as presented to DD sound at all healthy. Yes - one day she may suss things out for herself, and yes, she may feel angry with her mother, but equally, she could also feel furious with her dad for being lied to. Potentially, he is storing up a whole heap of trouble, and statistically, given she spends most of her time with her mother, it's more likely (than her hanging herself) that she (the ex) will be able to concoct a convincing story regarding all the secrecy and it will be DP, not her, left with the brunt of DD's anger/confusion/hurt/feelings of betrayal. It would obviously be so much better for all concerned if there were no secrets and no lies.
Of course DP is frightened that if he doesn't toe teh ex's line, she might start to get funny about contact, but legally she cannot dictate who DP introduces his daughter to whilst she is in his care. After all, does he dictate to the ex who she can keep company with, or who gets to meet their daughter ? ...... of course he doesn't, so you can see the whole situation is bloody ridiculous, and probably driven by the ex's urge to maintain "control" and/or spite/jealousy at the fact her ex-H has moved, whilst she hasn't. The only legal way she could demand that you were not to meet DD would be if you were a danger to her - you would need to be a drug addict, a violent criminal or a child abuser.
He has got to stand standing up to her because the whole arrangement is unnatural and hugely offensive to you - his long-term partner. If she got funny about contact, he would then need to obtain a court order specifying when he can see his daughter .... and the ex would need to come up with a very good explanation in court if she didn't want DD to see you, or come to her dad's house. The likelihood of that is practically nil - to prevent contact with you she would need accusations of serious gravity, which would easily be disproven, thus discrediting the ex completely in the judge's eyes.
The 64 million dollar question though is whether or not your DP would be prepared to take this next step - that of telling his daughter the truth, and attempting to arrange contact on his terms (which would hardly be unreasonable). If he refused point blank to do that, then you are left with a very unenviable choice ...... you either put up with a situation which is obviously causing you a great deal of hurt, or you get out of it. I appreciate neither is a very attractive option, but I would be questionning whether or not I could bear to be effectively excluded from being a full and respected member of my partner's family for quite some years to come - if he's not ever planning to "tell" DD about you, then it is feasible that she won't actually ever find out about you. How would you feel, for example, if, in the future, your partner attends her wedding and he is still pretending you don't exist ? Ditto when he's visiting his 1st grandchild ?
Unlike some of the responses you've had, I don't blame you for feeling very hurt by this. It hasn't come across to me that you are jealous of a small child per se, but are hurt that there is a hugely significant area of your partner's life from which you are excluded. Most people whose partners already have children accept there will be times when you take second place but this is entirely different. I totally understand you feeling that you partner shouldn't be able to have it both ways and I feel at best he has been tremendously tactless by waxing lyrical to you about the great time's he having. If I was told that I was totally banned from any aspect of my partner's life, and no, I couldn't come, I couldn't join in, it was "nothing to do with me" and so on, then whatever it was, I damn well wouldn't then want to hear him prattling on about it.
Unfortunately, I do feel that the time for an ultimatum (if you can't live with things this way) is very close. I'd temper that suggestion by saying that it might help you (both) to discuss these issues with a counsellor before that. If my partner was behaving like this, but refused to consider counselling, then I suppose I'd have my answer.