Star in the East

Scripture Matthew 2:1-2:
There came wise men from the east to Jerusalem, saying, Where is he (the child) that is born King (the Messiah) of the Jews? for we have seen his star in the east, and are come to worship him.

Interpretations:
for we have seen his star [while we were] in the east, and are come to worship him.
for we have seen his star [which was] in the east, and are come to worship him.

My Understanding:
The first is the way I read it and implies that they saw the star in the west while they were in the east. Whereas, the second says that the star was in the east with them.

Scripture Matthew 2:9-10:
When they had heard the king, they departed; and, lo, the star, which they saw in the east, went before them, till it came and stood over where the young child was. When they saw the star, they rejoiced with exceeding great joy.

Interpretations:
When they had heard the king, they departed; and [now let us explain how they got to this point], lo, the star, which they saw [while they were] in the east [upwards of two years previously (v. 7 and 16)], went before them, till it came and stood over where the young child was. When they saw the star, they rejoiced with exceeding great joy.
When they had heard the king, they departed; and [immediately after leaving king Harod's presence], lo, the star, which they saw in the east, [came back and] went before them, till it came and stood over where the young child was [in Bethlehem]. When they saw the star, they rejoiced with exceeding great joy.

My Understanding:
The first again is the way I read this and implies that both interpretations of verses one and two can be correct. First, because of verse 7 and 16 it is clear that it took the wise men some time after the birth to arrive, upwards of two years. So the second reading is extremely unlikely because the star would not likely be something they saw twice, while they were in the east and then again up to two years later, the moment that they made it to Jerusalem and showing them to go to Bethlehem which they found out from chief priests and scribes.

Summary:
The wise men, we don't know how many, were in the east when the star appeared. They may have seen it above them while they were in the east but it went before them to the west over the land of Jerusalem, specifically Bethlehem, where the young child was. It is assumed that the star appeared the night that Jesus was born with a confirmation from the Book of Mormon that this is likely the same star that was seen in the Western Hemisphere indicating the birth of the Messiah. It took the wise men some time, upwards of two years, following the path that was shown them by the star, to arrive at Jerusalem. They did not know exactly where in the Jerusalem area so they inquired of the king to know exactly where the young child was.

Other reference:
Hymn 210
With wond’ring awe the wisemen saw
The star in heaven springing,
And with delight, in peaceful night,
They heard the angels singing:
Hosanna, hosanna, hosanna to his name!
By light of star they traveled far
To seek the lowly manger,
A humble bed wherein was laid
The wondrous little Stranger.
Hosanna, hosanna, hosanna to his name!

My Commentary:
This hymn is doctrinally inaccurate but not critically so. First, if a springing star is a flickering star then there is nothing wrong with the use of this artistic license. Second, there is no indication that the wise men heard the angels. Third, the wise men did travel far because of the star but not by the light of the star. The idea that they traveled by the light of the star implies that they traveled all night and arrived the night of Christ's birth. This idea is strengthened by the rest of the verse.
This song is clearly a combination of the misunderstood experience of the wise men with that of the the shepherds.