Sorry, I haven't read all of this thread, but felt I had to post...
Can your DP and his Ex talk? Could he request that they meet (with or without mediation) and discuss how the hand over will go?
It's possible (and again, I apologise if this has come up but I don't think it has) that his ex is desperate to keep DD in her life and therefore prepared to do anything for her to ensure that... Perhaps if your DP could talk to the ex and have her understand that this will not happen, she might calm down a bit.
This probably won't be popular on MN, but here goes: My DH acts just like this around his DDs. GIves them pretty much anything they want, lets them stay up far too late (so much so they are grumpy little shits madams the next day) eat the wrong food, no manners enforced etc.,
He does it because his time with them is so limited and he's so worried about the relationship he does have with them being sabotaged (Jammi is in a similar position) so he goes along with it.
The kids have his passwords to i-tunes and ebay etc., and just buy stuff which is then charged to him. I don't know that he even checks.
I always defer to him re. the kids, as they are my DSDs and I've had times DSD1 has had boys in her room (huge no-no for me) and also stayed up way past 11pm (I was 38 weeks PG at the time and went to bed far earlier!!)
BUT (and this is a good BUT) If they were here full time, he'd never do it. He's a really good dad. He is, he's just desperate to (i) maintain a relationship with his girls and (ii) to enjoy the (very small) amount of time he actually gets to spend with them.
It might be worth a shot (surely it has to be) for your DP and his ex to try and work something out?
Anyway, just wanted to add that, for whatever it's worth.