You are correct. In English, if you have a phrase like this which can potentially modify two different things in the sentence, it will generally apply to the nearest one.
In many cases, we don't run into this problem, but in this case, part of the complication is that "earlier" could be either an adjective (modifying "date(s)") or it could be an adverb (modifying "came" or "seek"). This is technically ambiguous, but in reality it's not that confusing because adverbs are usually placed right next to the verbs they modify, not after other prepositional phrases, so if it was actually intended to be an adverb, it would be phrased something more like:
she came back 10 days earlier than I wanted with flying dates
(Note that in this case, you've also got some clues from the context. "After a week of inaction" already implies that things were taking longer than expected, so it doesn't really make sense to then say that she came back earlier than expected, so it's pretty clear that it must apply to the ticket dates, rather than when the action happened.)