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After the Babylonian and Assyrian Captivity, the bulk of the Old Testament Church (which was primarily Jewish, at the time -- but even in the Old Testament, there were non-Jewish members of The Church Universal) was returned to the Land of Israel, in preparation for the coming of the Messiah (the Second Adam, the Second Joseph, the Second David) Jesus Christ.

Thereafter, as a result of the Incarnation, Crucifixion, and Resurrection, "God's Israel" (comprising the believing Jews and Gentiles of The Church) do "seek the LORD their God, and David their king; and shall fear the LORD and his goodness in the latter days" as Hosea prophecied.

OP: The return you identify with the restoration of the Babylonian and Assyrian captivity occurs in the "later days" according to Hosea. You have inserted a parenthesis yourself in order to try to handle the text.

Your parenthesis...

For the children of Israel (Church) shall abide many days without a king, and without a prince, and without a sacrifice, and without an image, and without an ephod, and [without] teraphim:
Afterward shall the children of Israel (Church) return, {{Several centuries elapse until the Birth Crucifixion and Resurrection of Jesus}} and seek the LORD their God, and David their king; and shall fear the LORD and his goodness in the latter days.

My parenthesis...

For the children of Israel (Abraham's descendants) shall abide many days without a king, and without a prince, and without a sacrifice, and without an image, and without an ephod, and [without] teraphim: {{WE ARE RIGHT HERE TODAY}}
Afterward shall the children of Israel (Abraham's descendants) return, and seek the LORD their God, and David their king; and shall fear the LORD and his goodness in the latter days.

If there is not a parenthesis in your interpretation then the Return under Nehemiah = the later days.

And I commend you for dealing more intensively with the text. Refreshing.

OP: The return you identify with the restoration of the Babylonian and Assyrian captivity occurs in the "later days" according to Hosea.

Actually, to be a bit more precise, the restoration occurs:

"Afterward shall the children of Israel return,"

And sequentially thereafter shall "seek David their King" (i.e., Jesus) in "the latter Days".

"and seek the LORD their God, and David their king; and shall fear the LORD and his goodness in the latter days."

Remember, to an Amillennialist (which is to say, the Biblically-correct and Patristically-approved 2,000 year tradition of the Church), everything after the Resurrection is pretty much the "Latter Days".

Sorta like the World War in the Pacific after Midway, it may be a long and hard-fought battle -- but the tide is already turned, it's all "despoiling the strong man's house" from here on.