(Getting info out of the kids would be persuasion, but I would have only made the roll if they were inclined to resist in the first place. I'm pretty lenient when it comes to whether a roll is needed or an act just succeeds.
The only checks that could really "compel" someone to do something would be Persuasion and Intimidation, but I caution against treating these skills as a form of charming or mind control. Even if you "succeed" that doesn't necessarily mean the target is going to act in the manner you desire. For example, persuading or intimidation a hostile creature might get them to talk, but they could lie, lie by omission, only obey you temporarily or begrudgingly, etc.
Performance, basically says how well you can act, dance, play music, tell a story, or in general entertain someone. Some practical examples could be:
- Attempting to win a music contest;
- Pleasing a grumpy King who demands you tell him a story to lighten his mood;
- Performing for money;
Now, you could use these in conjunction with each other. For example, whether or not you succeed on a persuasion or intimidation against a character depends on their disposition toward you (friendly, indifferent, hostile). Their disposition (roughly) sets the target number you have to roll, and limits the degree to which they are willing (at all) to act in your favor, or at least not act against you.
A sufficiently adept performance could alter their disposition toward you and the party, making them more willing to help you later or provide information. Either by lowering the difficulty of success or by granting you some form of situational advantage, or simply by making it so they help you of their own accord.
All of the social/charisma-based skills are somewhat wishy-washy. If you want my opinion, persuasion and intimidation would be more practical from a mechanical standpoint than performance, but it is up to you whether or not you want to optimize your character for mechanics or choose the skills that are appropriate for them in a thematic sense.)