Legal scholars debate whether a sitting president can be indicted or only impeached. If the latter, it’s not clear given the statutes of limitation on most crimes whether he could ever be prosecuted for certain crimes. That surely seems wrong; the framers certainly did not intend to give the president a get-out-of-jail free card for crimes he might commit in office. (One solution might be to indict under seal.)
What is clear, however, is that to the extent the president has a safe harbor for prosecution during his time in office, that protection is personal to him. His relatives and his business empire don’t get that benefit.
Indict a corporation (or a foundation or an LLC)? That’s what happened to the accounting firm Arthur Andersen in connection with the Enron scandal. The firm itself was indicted on a charge of alleged widespread obstruction of justice.