Can a prepositional phrase starting with "during" work as an adjectival phrase?

As noted in comments, a prepositional phrase using during can be used to modify a noun. The example used during the day to modify work used as the subject.

The problem with your sentence lies elsewhere: it’s that during doesn’t work very well for plans. One has plans for one’s vacation, not “during” it.

Plus during the vacation sounds funny for other reasons. It is hard to construct a context where the vacation works at all; it doesn’t work like the holidays might. I suppose you could say during the summer vacation to mean over the summer vacation, but I would leave out that the myself and just say over summer vacation.

For example, these all work:

• I have plans for doing something special during my vacation this summer.

• I have plans to do something special during my vacation this summer.

• I plan to do something special during my vacation this summer.

• I plan to do something special over summer vacation.