My worry OP would be this one.
Your DP clearly has seen how she abuses his kind nature towards her DD. And is exploiting this. He knows this, but like you said has told you that he worries that if he tells her he is now seeing someone new, she will go balistic, and take it out on her DD by withdrawing contact or via emotional blackmail.
This has zero to do with the child, and all to do with the mother and what she needs, aka pub outings and any extra cash there is regardless of who the father is. Of course she was going to attempt to dig deep into his pockets, she has a lifestyle to maintain.
This can be draining on any relationship, and the ex knows full well that by demanding his time when he has free time, she thinks that she can then halt all his plans to see other people, and keep him at arms length for when she needs him. It has zero to do with the child, again its all about what this ex can get. I am sure that ones she finds out that your DP has you, she will punish him and her DD. And there will be emotional blackmail to maintain whatever she can regarding your DP and the things he is doing for her.
These things can get ugly, and your DP has probably seen it first hand and is therefor anxious going forward. I would try and support him in any way possible and show him he is merely a cashcow and babysitter.
What your DP does now in his private life does not need an explanation to his ex, non whatsoever. He should put his foot down and claim his life back, and give reasonable access to himself, not every weekend.
If you two are going to stand a chance he will need to sit his ex down, tell her things are changing, and stick to it, regarless of any threat of withholding contact, or whatever she may come up with, and he needs to realise that he may loose here by getting into another relationship, and that is something he is fully aware of by the sounds of things.