Who does the bolded part refer?

especially, this "grown-up" has a hyphen in between. This puzzles me.

Yeah, you're right -- the hyphen should not be there. But the phrase itself refers to Dorothy and her family. Her family no longer has any young children in it (They are now grown-ups). It's an awkwardly written sentence, grammatically correct but a little bit tortured in that it tries to get in too much information all at once. For example, the fact that she has experience in "having run a company of actors" (whatever that means) and having operated an antique shop seems to have no relevance to her new commitment to writing for children. But, there you are.