OP, I get that you are being put in the middle by your DP complaining to you about his daughter and I agree that some if her behaviour is unpleasant.
Some of what you have outlined really isn’t that bad, though, and as you weren’t there you don’t know how it played out- your partner may have contributed to the situation too, for instance. Of course , it may all be down to her being rude/entitled etc. And calling her father useless is very rude, she definitely should know better.
I think it is understandable that his DD was upset and hurt on hearing your comments (however accurate or otherwise they might be)- I think most of us would be, even if we could recognise that some (or all) of the comments are at least partly accurate. If you consider that she thought you got on well then she hears you criticise her- and may well have thought from the tone that you weren’t purely commenting on this individual event and more your opinion of her- and then thinks “well if that is what she really thinks of me, she’s really two-faced” and decided that she doesn’t want to have any sort of relationship with you. In that context, I think it was an upsetting thing to happen- even if you were “right” about her behaviour- I have some sympathy for her hearing your true thoughts about her when she thought you were getting on well. She could be any combination of very hurt, angry and embarrassed- has your DP said anything about how she feels, other than she won’t see you?
I was also struck by how many times you have cited your children/your parenting as a more favourable comparison to her and how your DP parented her. I think you need to be careful about making comparisons to your own DC, how their upbringing was superior to hers and their behaviour and thoughtfulness infinitely better than hers. Might be true, in your view, but it might be coming across as somewhat unpleasantly judgemental or a bit smug- “of course, MY children would never be so rude/always put others first/would never do x/y or z”. Whether true or not, it might not come across well to her or DP, the latter may then be more defensive of her. If his DD has picked up on your feelings, then heard this, it might be even more hurtful.
I think most people think the way they parent is the best way to do it and their children are “good eggs”. I’m sure your DC have had their less than perfect moments too.
it’s also clear that if this rift is not healed somehow it is going to negatively impact on your relationship with DP. He is going to have to miss out on things with one of you- birthdays/Christmas/family events- and you won’t be involved in her life in any way. Which might suit you, if you don’t like her, but I imagine is going to be hard and painful for your partner. He does need to do the groundwork for any sort of reconciliation, but perhaps you do need to examine if there is anything you could have done differently/are sorry about? I’m not saying give a grovelling apology to his DD, but perhaps to ease a reconciliation should she agree to meet halfway you might be able to offer something in return? Might be a case of you can stick to your view of being in the right, or give a little to move forward.