This is an over-nested sentence, with centre-embedding (as opposed the left-embedding, which is also frequently problematic, or right-embedding, which is less difficult for English speakers). The problem is that the modifying phrases are embedded into the centre of the larger one, so the cognitive burden is too much for the reader, who is trying to hold all the open phrases in their short term memory.
One solution for this kind of centre-embedding is to concatenate the clauses to form a simple sequence or right branching structure* instead of nesting them:
So instead of:
The girl whose mother had brought a fresh tray of delicious lemon cookie bars to class a week ago wrote a book report.
We can write:
A book report was written by the girl whose mother brought a fresh tray of delicious lemon cookie bars to class a week ago.
(Huh, that turned out easier than expected; am I mis-emphasising/missing something? I know it's passive, but it's not creating a dangling branch that need filling, so it shouldn't be a problem...)
Alternatively, to borrow Stephen Pinker's example from A Sense of Style:
The view that beating a third-rate Serbian military that for the third time in a decade is brutally targeting civilians is hardly worth the effort is not based on a lack of understanding of what is occurring on the ground.
can be turned into the far more understandable, if clumsy:
For the third time in a decade, a third-rate Serbian military is brutally targeting civilians, but beating it is hardly worth the effort; this view is not based on a lack of understanding of what is occurring on the ground.
which can now be split into two or more individual sentences that flow with the context (whatever it originally was).
TL;DR: All kinds of tortuous, weirdly phrased sentences that don't seem to cohere can always be improved by drawing a syntax tree** to sort out what the underlying units are and fit them together in a way that readers will be able to parse.
*a phrase where the complicated embedded bit is at the very end, so that the reader has already parsed the rest of the sentence. In left-branching languages, the opposite is obviously true. Japanese is the canonical example of a left branching language, if you're curious.
**of whatever sort - no theoretical assumptions required :-) or, if that seems like too much effort, using coloured highlights to find the phrases and relations.