I'm going to mention something that I don't think I've seen a singular poster touch upon before. I'm not playing devil's advocate for no reason, I genuinely think it's important to take these things into consideration.
These girls were just 12 years old, possibly even 11, when you took them on the first trip. The maturity, thoughtfulness, and responsibility of a 12 year old is awful, and the fact that they only mildly improved (showing up to dinner) at 13 is not a good sign, but not unsurprising either. Many studies show that children don't even develop abstract thought sometimes until around 12 years old, which is why kids can often be "selfish" and inconsiderate. Additionally, you aren't their parent and you have no clue how enabled their behaviors are. You cannot inherently claim a child is bad when they are not receiving proper parenting/punishment from their caregivers. Yes they are showing a bit more spoiled/bratty behavior, but I do agree with the parents and don't think that it's necessarily indicative of how they will be as adults. It could be if nothing changes, but you have the potential to give a good lesson here.
Additionally, I will say they're in their formative years now and might have drastic shifts in personality/behavior which many people do in their high school years. I do agree they shouldn't go on the Disneyland trip, but I feel like you should cut them some slack on the name calling back. You're 43 years old. It is unhealthy to refer to them as brats, salty, shitty, histrionic, spoiled, etc. At the end of the day, they're kids with bad role models that have taught them their behavior is alright. Kids don't even really develop abstract thought until around the 12 year old age.
Even though their cousin is better at every aspect of his personality according to you, you have got to stop the comparisons and the blatant favoritism. I'm not saying bring them on every trip, but treating your nephew like he's the bees knees and constantly spending time with him and lavishing him with affection while inherently considering your nieces spoiled brats, even if you bring them, is visible. Children are not stupid, just inexperienced. They will feel the resentment and how you care for their cousin more and like him more as a person, and this will ultimately drive a wedge further between you and have a lot less of a chance of you impacting their behavior in any kind of positive way.
Point being, everyone is joining in on the hate-brigade calling these two barely-teenagers awful and terrible for them going off by themselves on a trip and saying things are unfair and that life sucks when things don't go their way (being bought a swimsuit they really like, riding the horse they want to ride, etc.) But that's honestly common between teenagers, OP. The name calling is pointless, unhealthy, and contributes nothing to fixing their behavior or constructive criticism. I feel like the resentment for these kids is a bit too strong and that needs to be checked as well. Remember you're the adult and they're the ones learning and developing.
Also, right now you are acting infuriated over the family but you haven't even talked to the teenagers. You're basing all of your feelings about assumptions on how they'll act. And you know what, who wouldn't be hurt over their aunt going to disneyland, bringing their cousins and all of his friends, and then telling family about how it is because your nephew treats you better and you think he's a better kid. Then of course any negative expression of hurt is just again going to be considered "selfish" and "entitled" from your book. They're 14. This will destroy them and potentially damage your relationship for a long time.
Honestly, OP, if you want to teach them a lesson they have to know what they're being punished for. You can't expect them to learn like adults and behave like adults if you punish them like children and don't even discuss things with them first. Have a separate chat with them, communicate (politely, no name calling, even if they escalate by crying, feeling hurt, or saying it's unfair, as their feelings are honestly valid, it is technically "unfair" and will hurt their feelings but again has good reason) why you're not bringing them, and give them a goal for their behavior so they can actively work on it in the future. This way you two can build back trust and repair the relationship.
Right now you're wanting justification for not bringing them, and you have it. But honestly? You're not justified in the blatant favoritism and power-trip, and you're being as petty and immature as you claim these children to be.
They've also predicted that my nieces will never speak to me ever again when they find out which I feel would be sad but if that's how they want it to go, I'm willing to accept that
SERIOUSLY? They're 14! This behavior was done 1-2 years ago by them! Do you know how much development occurs during this point in time?
I feel like 14 is old enough to learn a difficult lesson
Yes, it is. Guess who has literally no clue about this lesson? Guess who has never informed the 14 year olds about what is happening and why (and who seems to have no intention about it, you just keep saying "when they find out, etc." because you're copping out of actually saying anything). Guess who literally cannot learn anything if they don't know what they're being punished for?
tl;dr Yes, OP, it's fine to not take them to Disneyland. But I will not condone your name calling, favoritism, skewing the writing to make the kids seem evil and you like a saint, and literally accepting them "cutting contact if that's how they want to go." You're acting immature, petty, and very unbecoming and quite frankly I feel like if this is how you treat these teenagers all the time, I absolutely know why they are not learning anything and why they probably don't feel as close to you or want to hang out with you. Just know this definitely will mark a huge deterioration in their relationship, and you know what? It's not all on them. They have the right to feel hurt, betrayed, and as though you don't love them as much as their cousin. Act like an adult about it and give them the decency of at least informing them of your reasons so they have the potential of learning something instead of just being punished so you can get your petty revenge on them for past behavior. Seriously it sounds more like you just want to punish them rather than help them grow or learn from their mistakes...