How do I deal with a stubborn co-author who won't respond to suggestions? My research group is preparing a theoretical article in a field where author order matters (computational neuroscience), and it has to be submitted soon, as our funding ends soon. I am an author "in the middle of the list." 

The first author (TFA) has made a first draft and started circulating it. Although results-wise everything is ok, the text is very poorly written (both in terms of English and general logic understandability). TFA is known to be not very responsive to even minor correction suggestions. 

Our PI knows the situation but he started his PI career relatively recently and his management skills have not yet fully developed, as far as I understand it. He says that he will just rewrite the whole text in the end (as he did with a number of other articles before).

Technically I or another middle author could rewrite the draft completely to make it better. However I think it would make the first-authorship of TFA somewhat strange-looking, and in general I feel that there should be some better ways.

So the question is: how are situations like this typically resolved?
Rewriting the text doesn't necessarily qualify someone to be the first author of a publication. If you're using the intended first author's structural outline and just rewriting sentences, then I don't know if that's sufficient to usurp the intended first author's claim. If I were the PI, I don't think I would do that.

What I might do is place a note in the paper along the lines of "X and Y contributed substantially to the writing of this paper," where X is the intended first author and Y is the person who rewrote the paper.

Better still would be for the PI to work with the intended first author about the corrections that are needed, rather than just rewrite everything. Helping X to become a better writer will reduce the PI's workload in the long run.