I'm no lawyer so maybe my input is less than useful, but I don't see why they couldn't be subpoenaed. Generally, in my knowledge trial attorneys tend not to subpoena witnesses they think will be too recalcitrant to give any good information, unless they cannot get along without the information they think they can solicit; or cannot find a more willing person to testify with knowledge of the same information.
From the point of view of pure privilege avoiding simply having to give testimony, the only such privilege is spousal. Parent-child is not a privileged anti-testimony category.
I have read about the family of the Loughlin/Gianulli. Sorry if I misspell their names, I never watch sitcoms and his designs I never heard about.
So I can't comment on their artistic qualities, it seems, average, since neither made that big a name, but it seems they are good businessmen, both of them.
From this standpoint, I think their whole behavior is neither entitled nor nasty, no, they simply weighed what would be good for business. They probably made a wrong decision, but they both seem to be rather emotionless and cold to me, so it probably was pure business.
About the kids, it, too, is pure business. Now they are mostly concerned about not losing own businesses and their daughter's sponsorships - or rather, since she lost some, are concerned about restoring them, probably?
So the daughter has to look good. To look good, honestly, she'd better not testify. If she shows up, denying any knowledge about the deal, given that they were photographed/photoshopped on rowing machines, and one of them posted something about not being into school, would be perjury. On the other hand, admitting own complicity would mean, definitely losing more sponsorship. Either way, it will look bad. So this is the parents' concern.
