The first -- "pulling the socks from behind" -- is better. As @stangdon says, the use of "backside" in the second version is ambiguous (it could mean the same as arse/ass). But even without that problem, it's simply the wrong word in that context.
But I actually think there's a third even better option: namely, "pulling the socks from the back". The reason is that your "from behind" in the first version is also ambiguous. It could be taken to refer to the position of the puller, rather than the position on the sock (on which to exert the pull). Of course context would show that it cannot be the puller's position -- how could you get behind yourself to pull down the sock? But "from the back" avoids the ambiguity anyway.