Interestingly, in the original draft of the the script, they were going to explore this theme.
There's a song (We Know Better) that was written which is Elsa singing to Anna shortly after she is born.
It's full of references about how much pressure there is on Elsa to live up to expectations as the future ruler and her fear that similar pressure will be placed on Anna as well.
This song didn't make it into the final cut of the movie, but it was still written and a demo recording exists (you can find it on the deluxe version of the soundtrack).
The secret to controlling Elsa's powers was
not the powers themselves, but her emotional state while using them. So regardless of how much she practiced, it would have done no good, since nobody knew the connection until the very end of the movie, when Anna tells the secret of control to Elsa (she learned it from the Trolls).
Ironically, Elsa thought the trick to controlling her powers was to suppress her emotions, when in truth, she had to embrace them in order to master her powers fully. Specifically, love and happiness.
What you discover at the end of the movie, by isolating herself from Anna, she's actually making the situation worse, allowing her negative emotions to feed the power.
If she'd just stayed happy, there would have been no problem controlling her powers at all!
Ariel was 7th in line, she was the youngest.
Ironically, despite that, there is a subtext that she was going to be the future ruler of the seas.
Something about how she was so much like Triton that she would have been chosen above the others, despite her low ranking in the order of succession.