The interpretation of how Hosea 11:1 uses Matthew 2:15 has a troubled history. Beale gives a short overview of interpretations before he offers his grammatical-historical and biblical-theological approach. Beale concludes that Matthew makes a comparison between Jesus as the "son" with the "son" of Hosea.
Beale addresses the New Testament uses of the Old Testament that appear to have a meaning inconsistent with the original meaning of the original context. Examples are: John 19:36 claiming to be a fulfillment of Exodus 12:46, and Hosea 11:1 in Matthew 2:15. Beale argues that Old Testament writers knew more about the topic of their speech act than only the explicit meaning expressed.
This article has extensive exegetical notes on Hosea 11:1-11 based on the original Hebrew.