As a seasoned parent of adult children and from 40+ years in medicine and psychiatry, a brief jail experience could only do her good.
Jail is a lot of things, but we do not believe jail experience typically results in childbirth or advanced academic degrees. Perhaps this naive; there are conjugal visits and prison libraries, after all (but probably not both at the same time.)
At any rate, what Dr. Klein meant to write was, "As a seasoned parent of adult children with forty-plus years in medicine and psychiatry, I think brief jail experience could only do her good."
The "as a seasoned parent" phrase must modify the subject of the sentence. As it's written, it modifies "jail experience."
It's hard to make this sort of error when using the traditional subject+verb+object syntax. When in doubt (or when posting something you cannot later edit), best stick to the straightforward. And when editing, beware sentences that start with modifying phrases. They're the mousetraps you've stuck in your own cupboards; you don't want to smack your own fingers when you're reaching for the crackers.
Another note: "Do her good" is grammatically sound. There is a grammatical unicorn galloping about that insists "well" must be used to modify a verb. The most common way this unicorn presents its mythical old self is when people say, "I am well" is the only correct response to the question, "How are you doing." This is false, pompous, and silly.
English is a flexible language in many ways, and especially with its parts of speech. Good here is a noun. It's what's being done, not how.