OP, I feel you're being misunderstood by many of the people who responded. Also, it's clear a lot of people who replied are not in any kind of blended family, so they simply don't appreciate how the dynamic is different. Someone saying 'well I would never be jealous of my DH taking out our DD' is completely missing the point. Biological families are just completely different, the emotions are different, the hierarchy is different, etc. In blended families (whether you're living together or not) it's unfortunately often a zero sum game. No one wants to admit this, but I'm sorry it's just a plain fact of life. What's good for the partner is very often bad for the other person's children, and what's good for the children is often bad for the partner. That's because resources are finite (time and money being the most in demand!) so you can't give more to one side without giving less to the other, and that makes blended dynamic very different. The interests of mum and dad in a biological family are always going to be aligned, pointing in the same direction, with their children at the apex. That's normal as it's their children. When the children are not in common, it becomes much more complicated, because you have two people in a relationship, but each person's strongest interest is pointing away from the relationship (their own kids).
I didn't for one sec think you're accusing your DP of something pervy, you wouldn't be with a monster! It's clear this is simply a man out with his daughter.
I understood you more as questioning whether these places are meants for such young teenagers, and also whether by 'upgrading' their outings from (as an example) Nandos and bowling to, now, fancy restaurants and cocktail bars, her dad is letting her kind of step on your territory, especially if he's taking her to your favourite places. To be completely honest, he shouldn't be doing that. There should be some kind of line between what's yours and saved for special romantic dates, and just general places where he can take her. But he's a bloke and probably doesn't think this way at all, and probably doesn't realise it these places are very special to you. He probably just her there as they are places he knows and he's too lazy to look for new ones (sorry).
Yes it's a form of jealousy on your side. Guess what? Jealousy is a normal human emotion and very common. It's an evolutionary response to feeling threatened, to worrying about losing something precious to us. Sometimes the sense of threat is unjustified or misplaced, as the case is here. But your subconscious doesn't know that, and that's where jealousy comes from. You can rationalise it, reframe is conciously. But it arises at a deep, instinctive level and you shouldn't berate yourself over it. What would help you is to find more opportunity to be alone with your DP so you and him can go on more dates.
In the meantime, don't forget that being a little bit jealous is far more attractive and honest as a trait than being self-righteous, as so many of the responders have been!