I really don't think she has anything to worry about from her parents.
You wrote that you wouldn't want to be questioned by the Secret Service, I don't think you would threaten the President regardless of your personal beliefs.
Yes there is due process, but you can be detained for reasonable suspicion of a crime so long as the detainment is for a reasonable time. I did not read that they kept her locked in a room for thirteen hours. I gotta say making threats, even in jest, against a sitting President meets the reasonable suspicion standard.
No, I wouldn't, but I am aware that IF I made a stupid nasty threat online I would expect the authorities to show up at my door to question me.
As previously stated, if I was a minor, I wouldn't want to be questioned without my parents present. As a parent I wouldn't want my child questioned without me present either. If the Secret Service were to show up at my door for any reason, I would not want to be questioned without my lawyer present--that is my right, and yours.
The flip side to all this is that anybody can post anything online with your name on it and you can find yourself falsely accused, and that happens a whole lot more than you may think. Conservatives seem to have a block of wood in front of their faces when it comes to certain constitutional issues. I'm not one of them. We are supposed to be presumed innocent until proven guilty in America, though the reality is quite the opposite.
This little girl did a very stupid thing, and she and her parents got a good lesson in how things really work. I hope they learned it.