‘And Ephraim is like a silly dove,
Without understanding,
They call to Egypt,
They go to Assyria.'
Ephraim is depicted as a hapless, fluttering bird, which, ignorant of what was best for it (genuinely and submissively calling on YHWH, and on Him alone), at one moment ‘called' to Egypt (instead of to YHWH), and at the next went to Assyria. Thus they are simply a ‘silly dove' compared with the great eagles, Egypt and Assyria (Hosea 8:1; compare Ezekiel 17:2-10 for the idea). This was a true picture of the situation. They ‘called on Egypt but went to Assyria'. For when Assyria was strong and had no distractions elsewhere they had no real option but to ‘go to Assyria'. But inevitably they were never happy with their enforced subjection so that they would almost certainly keep in touch with Egypt (who were wary of Assyria's might), with the result that at times the promised support of Egypt (which never directly materialised - Isaiah 30:7) encouraged them to refuse tribute to Assyria. And the point behind YHWH's words is that all this happened because they had not trusted in YHWH, and indeed that their very submission to the requirements of history was evidence of their rebellion against Him. Why else did they think that it had happened?
We can see all this from the very abbreviated history in Kings. It began when Menahem submitted to Tiglath Pileser III and paid tribute, which he obtained by taxing the rich men in the realm (2 Kings 15:19-20). But when Menahem died and his son Pekahiah began to reign, Pekahiah was almost immediately assassinated by Pekah, who was probably already a petty king in Gilead and wanted to break free from the Assyrians, and now aimed for the full kingship of Israel. In consequence of supposed Assyrian weakness (they were being distracted by events elsewhere), Pekah ceased paying tribute to Assyria and united with Aram (Syria), and probably other nations, in an alliance aimed at resisting any Assyrian reprisals (Isaiah 7:1-2; 2 Chronicles 28:5-21). There was probably an understanding with certain elements in Philistia, (suggested by what happened when Assyria did finally retaliate, and by 2 Chronicles 28:18) which would almost certainly have included contact with Egypt (who would promise anything in order to cause trouble for Assyria).
Eventually, however, Shalmaneser V (Tiglath Pileser's successor) was free to retaliate, and having defeated the Philistines, took over the northern part of northern Israel, turning it into an Assyrian province and exiling many of its inhabitants (2 Kings 15:29). It was at this point that Hoshea seized his opportunity, and, probably with assurances from Assyria, assassinated Pekah and sued for peace. This resulted in his becoming a subject king paying tribute to Assyria, something which saved the southern part of northern Israel (Ephraim) from the fate suffered by their northern counterparts. But eventually Hoshea (no doubt pressed by his advisers and princes) tired of Assyrian rule (it was very expensive) and entered into secret negotiations with Egypt (2 Kings 17:4). This resulted in his withholding tribute from Assyria, and in consequence in the final destruction of Samaria, with the cream of Israel taken into exile (according to Assyrian records over 27,000).
The corollary of all this was, of course, that if only they had been full-heartedly trusting in YHWH, and in YHWH alone, none of this would have happened, because YHWH would have delivered them from the might of the Assyrians.