Your sentence is grammatical. "Being well-treated" is an introductory participle phrase used as an adjective to describe the subject of the main clause (she).
That being said, it is a little bit difficult to figure out for certain what you actually mean. It's not entirely clear what "being well-treated" would have to do with getting home sooner. If someone said this to me, I would guess that "well-treated" is supposed to mean that she received fast or expedited service, but that's not necessarily what it means, and you might not mean that at all, so it's ambiguous.
I would suggest being more explicit with something like:
Having received expedited service, she was able to return home earlier than she'd expected.
If you want to keep the idea of "well-treated" in there, it is possible with something like:
Having been treated to expedited service, she returned . . .
"Expedited service" sounds just a little stiff, but I can't guess at ways to improve it without more context. Although more context might also make it clear that no causal relationship is implied here at all.
When speaking about medical treatment, you would not usually talk about "expedited service," of course. To clarify, there's nothing wrong with introducing a sentence with "being well-treated" or just "well-treated," whether you're talking about customer service or medical treatment.
The problem that causes ambiguity here is the meaning of your main clause, because good treatment doesn't usually imply fast treatment or explain in any way why she got home sooner. However, using a different main clause as an example, both of the following are logical and grammatical!
Being well-treated, she made a full recovery.
Well-treated, she made a full recovery.
Note that this also makes sense:
Well-treated, she made a speedy recovery and was able to return home even earlier than expected.
Now it is implying that the very excellence of the treatment caused her to recover faster, rather than implying there was something fast about the treatment itself.