So what if they are God's "arbitrary whims"? As long as they are God's whims, there's no problem.
As long as God is defined, among other things, as the source of morality, as the source of your moral sense, there's no problem.
The whole idea behind "God is the source of morality" is that our human sense of morality is per default given to us by God, inherently, just like God gives us our bodies; it's not like we are somehow independent, self-sufficient beings in a universe created and maintained and at the "whims" of God; nor is it the case that we are born as amoral beasts and then need to be taught about morality from religious figures.
Sorry, but you don't see the contradiction there? If God's "arbitrary whims" are not a problem and they are in fact whims, then God cannot be the source of any morality, nor can we be anything other than whimsical when it comes to our morality. Of course, that is exactly what we observe from religionists; whimsical morality.