Are both theses sentences correct and commonly used:
“Kick the ball to me.”
“Kick me the ball.”?
Neither ODO nor OED give kick a ditransitive sense where there are both direct and indirect objects.
Google Ngrams don’t find kick [pron] the ball for various values of pron like me, him, them. (You can’t use the
_PRON_ part of speech in a four-word ngram, so I had to do each individually.)
So it appears that it is not used, and if one can take a dictionary definition as “strict” then strictly speaking it would appear to be ungrammatical. That said, as Janus commented, it’s entirely understandable even though it’s not idiomatic.
As to why it’s unidiomatic, I suspect that it’s because me following a verb is more easily taken as a direct object unless that can immediately be seen intuitively to be unlikely. Thus when you hear “Throw me the ball,” the brain hears me and can decide “Throw me? I’m too heavy, me must be the indirect object,” even before it gets to process “the ball”. On the other hand, “Kick him the ball” works in exactly the opposite way: it’s more likely to process him as a direct object, and then get discombobulated when the real direct object appears. For this reason, children learning the language by immersion will mark the form as difficult and not use it. Because it’s not used, kick never develops into a ditransitive verb.