Reason 1: the Curtis parents and the king and Queen of Arendelle died in very similar ways.

In Frozen, the king and queen died when their ship sank. In The Outsiders, (or I guess before if you want to be technical) the Curtis parents died in a car accident while we can assume they were taking a trip, as a scene in the movie shows them packing luggage into their car right before showing the wreck, so they probably weren't just heading out to the corner store or something. In both cases, the parents were going on a trip, and either died before they got to their destination, or coming back. Also, both couples were alone on the trips, as we know Anna and Elsa weren't on the boat and Pony never mentioned him or his brothers being with his parents when they crashed, and being in the same crash that killed your parents doesn't exactly seem like something you'd leave out when explaining how they died. I mean yeah, sure, lots of books and movies have the parents of the hero or heroine die before or during the story, but how many of them have the parents die in an accident involving a mode of transportation, on a trip, without their kids? Sure this reason is kind of a stretch, that's why it's the first reason.

Reason 2: romantic interest implied, but not quite canon.

Sure at the end of Frozen Anna and Kristoff do kiss, but their romance isn't quite canon (almost but not quite). The movie ends with their relationship could really go either way, but in canon they're simple headed to that point; they most likely will end up together, but not in canon. Also in The Outsiders, it's implied that Cherry and Pony could possibly end up together, but they weren't more than friends at any of the time in the book. You might say that Cherry would never want to be romantic with Pony, but consider this: Cherry is around sixteen, and girls around that age want to fit in and be popular, especially girls in the upper class, and in the society she lives in, dating a greaser would make her an outcast. Both characters are very compatible and if it weren't for the socioeconomic divide, they could very likely be an item; in fact, based on Cherry's actions toward the gang, they could be headed that way after the book takes place. But in both cases, the romance isn't quite canon, but it's definitely headed that way.

Reason 3: let it go on the mountain.

When Pony and Johnny run away, they find asylum in an abandoned church on Jay Mountain. When Elsa runs away, she finds asylum in her ice castle which is also on a mountain. And in both cases, being alone on the mountain, safe from everyone back home who wants them dead, makes them stronger; they find what's been hiding inside all that time they were acting how society told them to act, and learn to let it out.

Reason 4: things start to fall apart back home as a result of the actions of the hero/heroine.

When Elsa unleashes an "eternal winter", Arendelle starts to fall apart, and her and Anna almost lose the kingdom. When Johnny killed Bob, even if it was just self defense, the tensions between the socs and greasers grow so much that Dally has to carry a gun around to scare off anyone who tried to attack him- Dally!-, and they have the rumble to settle it all. So in both cases, when the hero/heroine runs away, things start to go south back home.

Reason 5: don't let them in, don't let them see; one wrong move and everyone will know.

That part of the song "for the first time in forever" where Elsa was singing the whole "don't let them in don't let them see"  thing could be swapped with what Darry said to Soda and Pony before the rumble because both him and Elsa were trying to hide something from society because if they didn't, something bad might happen. In the beginning of Frozen, Elsa strikes her sister with ice, which motivates her parents to lock her away so nothing like that would happen, so as a result, she is scared of her powers. While Darry isn't scared of him or his brothers fighting, he tells his brothers to run if they hear the police, and when the three were reunited at the hospital, he cried because he had thought Pony was gone, and at the beginning he slapped Pony because he had been out too late and Darry was getting worried. So Darry was afraid of losing the rest of his family, and the kind of things him and his brothers were involved in could take them away, just as Elsa feared that if anyone knew about her powers they would kill her.