What is the meaning of "rocking him sideways" in the sentence below:
An ice-cool sensation entered his mind, rocking him sideways. Hilda’s hand was in his.
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This is actually interesting because the usage you quote is slightly surprising. The verb "rock" has two versions, the transitive and the intransitive. The intransitive is more common: something that rocks is something that wobbles back and forth in place. But there's this transitive sense, where to rock is to make something else wobble back and forth in place, and that is the sense invoked here.
It's saying -- and it may mean this figuratively -- that the "ice-cool sensation" gave him a sideways shove. In English we sometimes use kinetic idioms to express how strong emotion something provoked. I recently had occasion to say, "Today I taught someone a different way of thinking of housekeeping that rocked his world," which is an idiomatic expression that means it both caused him enormous surprise and astonishment but also great positive excitement.