For whatever it is worth, my son started to have similar tantrum problems when he was a toddler. Although I am not a behaviorist, I figured Skinner might know something, so I set about to extinguish the behavior according to behaviorist practice. It worked.
I did so as follows: When my son began engaging in tantrum behavior (falling on the ground, screaming, kicking, holding his breath, etc.) I first made sure he was in a situation where he would not hurt himself, then I left the room or otherwise totally ignored his behavior, giving him ABSOLUTELY NO ATTENTION WHATSOEVER, until he resumed normal behavior and stopped tantrumming. I did this consistently, without fail. As a result, he only had about three or four tantrum incidents, total.
The theory behind this strategy is as follows: If you reinforce the negative behavior by giving the child what he wants when he engages in the negative behavior, you teach him that the negative behavior works and gets him the results he wants, so he will do it again and again and again. Even negative attention (yelling, spanking, getting upset) serves to reinforce the bad behavior. What's more, intermittent attention to bad behavior (e.g., reinforcing the behavior some of the time and ignoring it some of the time) sets up an intermittent reinforcement schedule, which makes the behavior almost impossible to extinguish because he learns that if he keeps up the behavior you will eventually relent and give him what he wants as a result of the bad behavior. Only when the child CONSISTENTLY gets NO attention (none, zero, zilch) for the bad behavior, he learns that the bad behavior is useless, stops doing it, and looks to other types of behavior, hopefully more positive, to get what he wants.