An explanation by William H. Shea:

The return of the Jews under Ezra is described in chapters 7 and 8 but their rebuilding of the city is described in chapter 4. Why are things out of order like this?
It should be pointed out here that there is more than one way to organize a book, biblical or otherwise, and the author does not always have to subscribe to the strictly chronological approach. He might also follow a topical approach. And that is what has happened here. There is a parenthesis here between Ezra 4:5 and 4:24-5:1. The parenthesis continues its own recital along chronological lines but the topic or subtopic being opposition to the Jews. That opposition is cited first for the reign of Cyrus in Ezra 4:1-5, then for the reign of Ahasuerus (or Xerxes) Ezra 4:6, then for the reign of Artaxerxes in Ezra 4:7-23. Then with Ezra 4:24 the narrative returns to the time of Darius, between the times of Cyrus and Ahasuerus.
The topic treated in this subsection (Ezra 4) is opposition to the Jews. The opposition is in the first case about building the temple (time of Cyrus), then a more general opposition (time of Xerxes), and finally an opposition about building the city of Jerusalem (time of Artaxerxes). Fensham has given a nice evaluation of this problem in his statement that,

In spite of this [the chronological order of Persian kings in chapter 4], Rudolph presumes that the Chronicler had no idea of the historical sequence of the Persian kings and mentioned typical names which are accidentally correct chronologically. Rudolph arrives at this conclusion because of the sudden switch to Darius in 4:24. . . . Thus it is understandable that modern scholars, reasoning from their own logic, should regard the historical reliability of this chapter with suspicion. But there is another kind of perfectly legitimate logic to the reasoning of the author of this chapter: he is referring in this chapter in chronological order to the hindrances placed in the way of Jews to rebuild the temple and the wall of Jerusalem. When he discussed the problems of the building of the temple in 4:1-5, it reminded him of later similar troubles with the rebuilding of the wall of Jerusalem, and so 4:6-23 has been inserted, almost parenthetically, before the argument of the building of the temple has again been taken up in 4:24ff. (already noted by C. F. Keil in the last century).[8]

Thus there is a perfectly good explanation as to why the decree and the return are described in chapters 7 and 8 but the rebuilding undertaken by the very same people who returned in these chapters is described in chapter 4. There is no conflict. The chapter arrangement merely reflects the author's decision to treat his materials in a topical rather than in a strictly chronological manner.

http://www.adventistbiblicalresearch.org/documents/Whendid70WksofDan9begin.htm

Aaah, David, we're all agreed that Ezra 7 is dated to 457BC. It'd be disturbing if our earliest literature didn't hold this position unanimously!!...

What about Ezra 4 and its dating???...

Yes, clearly Israel had to fulfil its promised purpose - accomplish God's plan for by receiving the Messiah, and the 70 weeks was that period for holding rightly to their faith and it reaches up to Stephen's martyrdom. The dating of Ezra 4 as you're arguing for is suspect simply because effective permission to build Jerusalem is necessary before the wall and temple of Jerusalem can fully be built:
Ezra 4 cannot pre-date Ezra 7 for this obvious, practical reason.

Impressive editions of Bibles are not authorities for the interpreted dates they insert, unless they interpret reliably. Well?

If chapter 4 is truly dated after chapter 7, then the King changed his decree to rebuild the city. For in chapter 4 verse 21 in the kings reply to the “father’s”, he states;
“Give ye now commandment to cause these men to cease, and that this city be not builded, until another commandment shall be given from me.”
The “fathers” had sent the king a letter in which the king was told that they were in the process of rebuilding the city.

We know that chapter 7 is dated in 457 B C, with the decree from the king to rebuild the city to Ezra. So here we have the decree to rebuild some years after the “fathers” had asked to rebuild and some people apparently had begun to rebuild the city without the decree to do so.

If chapter 4 comes some time after chapter 7 and it is an order from the king to stop work on the city, then is the date 457 correct? If so, and chapter 4 is a later date than chapter 7(457) then what is the date they started to rebuild the city? And will it still fit with the timeline of Christ?

I do not believe it so. In chapter 4 there is no decree from the king to rebuild the city, only an order to stop the unauthorized building of the city. Some thirteen or so years later Nehemiah also went by order of the king to the city although there is no decree to him to rebuild the city, for it was already being rebuilt, with the Temple of God being built first.

Peace and Grace
David

There is only one way that I know how to do this, and this is by showing that a decree went out and that also there was a rebuilding just after that date. Prior to the date of 457 did anyone act upon the decrees to rebuild the city?

Peace and Grace
David