>I have learned that the Docility trait is obtained from the drone.

 Bee breeding is a little strange but from what I have been reading in the
latest editon of the "hive and the honeybee" would seem to suggest that the
transmission of any genetic trait can come from both sides.

In bee genetics the male is, in most cases, a transport of his mothers full
genetic pattern. In other words you are directly crossing two queens into
the new offspring.