The house of David was retained as an inherited title in the southern kingdom thereby tracing legitimacy in rulership back to David. Ephraim is the lineage designation for the leaders of the northern kingdom. Thus when the southern kingdom is referred to by lineage (house of David) so the northern kingdom is referred to by its lineage designation (house of Ephraim).
In poetic language. the news of the union between the northern kingdom and Assyria is "moving." For the political reality of a close neighbor being aligned with another locally powerful state, the poetic language is understatement. Grave concern would be more appropriate than "moved." Perhaps the movement of the movement of the trees refers to the shaking of the leaves, and might refer to a symbolic shaking in fear.