Since only one parent died no need for a guardian. And really nothing else applies. It’s just one of those things that comes with minors earning money, especially in a contract situation. Since they’re minors they can’t technically sign contracts, so somebody needs to sign on their behalf, but given what happened to the child stars of yore there are safeguards in place to keep the person who signs on their behalf from spending the money. Really I’m surprised they didn’t see this coming, it’s not the first time she’s performed in public since he died, and those would probably be paying gigs. Maybe those gigs paid the foundation so they didn’t need to worry about it.
I think the situation here is that California requires protection for the child by both parents, and anyone else who claims guardianship of the child (like a step-parent) sign a release form.
In most of the world, indicating that one of the intended signers is deceased would be enough, but California probably requires an official certification of death.
But this was still handled in a ridiculous manner. All the judge had to say was “We’re all set. Just need to have the death certificate sent to us for the father and we have no problems.” rather than “You need to prove he’s dead.”