There is one other thing I noted in your method. I suspect Painted Horse's horses are already very obedient and willing to learn any command or cue, as evidenced by the fact that his cue for this move becomes simply a raise of his right hand, rather than a tap on the rear. Your horse, from your description of him pushing against your husband, is not. I also suspect that if PH's horse were to be so disrespectful, his "tapping" would be significantly harder than yours. His horses understand and respect that fact.
When teaching a horse any cue, giving the same tap, tap, tap, tap, tap, tap...etc. ad nauseum just irritates the horse and makes them ignore cues, rather than learn them. Give him the cue - say three or four quick taps. If no response, then give it again, this time a little stronger. Keep increasing the pressure (strength of the taps) with each series, until it becomes uncomfortable enough for the horse that he makes an effort to figure out what you want, so as to stop the discomfort.
The progression in the strength of the cues should be fairly steep, so the horse learns that moving the first time is significantly better than waiting for the next series. Then the praising comes in. It must be immediate after he gets even close to doing the right move at first, but doesn't need to be a five-minute loving session. Just a nice pat or rub and a gentle word, then start over. Require that his effort be more correct each time before stopping the cue and giving praise.
I also like what Golden Horse said about starting with teaching the cue on the off-side first, for your horse. Teach the horse the cue first, where you are in a position to really give a solid cue, if necessary, without putting yourself in the dangerous position of having the horse jump into you. In other words, if your horse isn't responding and you have to give it a real "whack" to get him to move his a...er...rear end, he may suddenly move very vigorously away from the signal. You don't want that move to be right into you standing there on a chair! After he understands the cue, then teach him to execute the move with the same cue, with you on the opposite side from the cue (left side), where he moves toward you, rather than away.