It is very difficult to wrap my head around this for sure. I don't think they had a death wish. IF the RR story is true, then my guess is that NH put one round in the gun and put the cylinder in a position where there should have been 4-5 trigger pulls before it fires. He tells KA this, so they both point the gun and pull the trigger thinking its safe. But NH has made a mistake and lost track of what position the cylinder is in. He points it at her thinking he has one more safe trigger pull before the cylinder advances the live round into firing position. But he is wrong and the gun goes off. I seem to recall that NH had boasted on FB or somewhere about having recently bought this revolver. He maybe just had very little experience handling it was unfamiliar with it. So, in this scenario, he didn't intend to shoot her. But I still think its manslaughter.
However, the whole RR story seems just crazy to me. So I don't rule out that something else entirely happened and the RR is made up. I don't think he intended to murder her. That would be crazy. In his apartment, on duty but out of patrol area, with a married woman, drinking on duty. Doesn't add up. NH needs to just fess up and come clean about what happened. I suspect that the full truth isn't really going to be too flattering to Alix, but whatever she was doing there, she didn't deserve to die.