.. a vampire with Dominate still can play Obedience even when successfully rushed by another vampire using Deep Song. The key for this is timing. Obedience is played "when about to enter combat" (i.e. before the combat), while Deep Song's effect that the reacting player's minion becomes the acting minion is actually taking place in the combat. So just before combat while the reacting player's is still reacting he can play the Obedience and thus avoiding combat and thereby the effect of Deep Song.
Secondly, the reacting vampire is not tapped by acting vampire's Deep Song, by playing Obedience he prevents the "enter combat" part and is therefore not tapped. As LSJ remarked, this is "similar to the case of another 'tap and enter combat' effect: a successful block".