im honestly not seeing any dominance issues twords the owner, has the dane ever bitten you?...how old is your dane? I have a 1 year old male great dane.. when he was a little pup he would let my smaller dog dominate him and boss him around, but once he hit a year he didnt allow her to do that to him anymore..your 2 are most likely establishing dominince between themselves, the dane is testing the basset..when your dane bit the basset, what was the situation? Was there a toy or food involved?