OP, I noticed that you are not the resident parent, so presumably your daughter visits at weekends etc.? A slightly different perspective follows....I tell this story not because I think you should accept your DP's behaviour - I think it's too late, you need to cut loose - but as a guide for your next relationship.
As a stepmum, I confess to having had some problems with my DP's children in the very early days. In retrospect, a lot of the problems were around 'who is boss?'; it was a whirlwind romance and I had moved in within 3 months of meeting my DP, and myself and the step-kids were kind of 'forced' on each other (by a lovely DP who BTW only had the best intentions, and lots of love to give everyone).
My DP had kept the family home exactly as it was when he was married and the DC regarded it as 'their home' and not 'ours' - the examples seems so silly now but at the time they were quite hurtful - stuff like the DS giving the ex-wife's sister a key (so she took to letting herself in for a nosey), or the DD borrowing my clothes without asking because 'mum doesn't mind'....
For my part, I probably was indeed jealous of his unconditional love for them. It was odd that he snuggled them on the sofa rather than me ...and before you all go loopy, of course I knew that I had him the rest of the time so he was just sharing his snuggles! It doesn't mean it was any 'easier'. I hardly sulked, but I admit to occasionally wandering off & reading in another room rather than sitting on a chair on my own watching kids telly!
As it happened, my MiL was the one who sorted it out - she spotted the signs within weeks & gave the kids a big lecture on trying to understand the new set-up, and then did the same to me! We all made a big effort around 'boundaries' and trying to understand how the other person feels, and 13 years on I would struggle to find a closer step-relationship than the one we all have now. DS has just gate-crashed a 'romantic' weekend away (at my insistence, I know he likes that city) and DS comes up most weeks for lunch while DP is at work....
The moral of my story is that it's hard being a step-parent at first, and you rely on the parent to guide you about how it all 'works'. Please make sure you set the boundaries & expectations for both parties straight away next time round, and you will have a wonderful & fulfilling relationship all round. Best of luck!