We are having the same problem with our almost 4 yr old, but in reverse. I'm the stay at home mom and he adores me but has been giving my husband a hard time like you have described, for close to two years. However, my son occasionally phases out for a week or two at a time and really enjoys time with his dad, and I thought I'd share my observations with you of what I see going on between the two of them because it may help your situation. My husband loves our son dearly but has never, in my opinion, chosen to invest much time with him. When he is home in the evenings and on weekends, he "must" watch the news or other shows, work on the house, or mow the lawn etc... Many evenings we have been all together in the same room and my son asks for his attention but Daddy is too busy or tunes him out. I've never seen my husband stop a task or turn off the news to play with him. He certainly does play with him on occasion, but it is almost always on his terms at his convenience. It is certainly not daily. This has been going on from day one, and as my son has exhibited the same behaviors you described in your son over the years, it has hurt my husband's feelings time and again. Over and over I have explained to my husband that he must elect to pay more attention to our son, and when he does take my advice and really works on it for a few days, at first our son resists it (most often in a mean way) but then suddenly he is all excited to do things with Daddy. I mow the lawn (my husbands favorite chore since he has a lawn tractor, by the way) so that they have those few hours together; they go to the hardware store together; they play cars... For a while I even got my husband to take him out to breakfast on Saturdays for some "guy time." But always after a while my husband makes excuses, slips back into his old routine and my son gets frustrated and it all goes back to status quo. I guess my point is, maybe your wife needs to look at the time she's home with your son, alone or otherwise, and see if she is giving him as much attention as he may need. I'm not talking about seeing to his regular needs, mealtimes, bathtime, discipline and such. I mean does she take time out to play with him every few hours or does he entertain himself, or watch tv, while she does housework during the day? If he wants her attention will she (without showing resentment) postpone what she's doing for half an hour and give it to him without distractions? Does she initiate playtime with him or always wait for him to ask for attention? While her in-home help is there, what does she do? Some kids need more emotional support than others (mine sure does) and if he senses that he is a nuisance or a burden to her, he may resent it. If she isn't focusing positive attention on him during the day, and then you walk through the door each evening and do, it would make him gravitate to you. With my son, I notice a huge difference in how he treats me, too, if I've been caught up in some task for a few days and don't spend the time with him I should. Sorry if this got too long, and this may not be what's going on at your house, but at least you know someone out here is going through a similar experience.
Unfortunately, you have described the situation with our son and daughter-in-law. This past summer, our daughter-in-law was diagnosed with OCD (a mental health disorder). Things have improved a bit since beginning medication but so far, no therapy has occurred. The "gap" between mother and child is growing and I fear for the future of this family. Could your wife be suffering from some mental health disorder? Please do not rule it out - our daughter-in-law hid her disorder for over 20 years, but as we think back, the signs were there - extreme anxiety, constantly changing jobs, constantly changing friends, being upset over minor annoyances, taking things out of perspective, lack of empathy, insecurity, extreme jealously/envy, and always, always making excuses (for anything and everything).
This situation is very difficult to handle because it is so discouraging and disappointing, to say the least, to not receive the affection of our children. Having said that, it is imperative that the parent who happens not to be in favor take the high road and not respond personally to the child or reject the child in return. Your description indicates that your wife has crossed that threshhold and is now acting angrily toward your son. It goes without saying that this sort of reaction will not only not solve the problem, it will exacerbate the problem.
For your part, it is important not to collude, so to speak, with your son by unwittingly encouraging his behavior. For example, it is not a good idea to defer to him at bedtime and 'let' him push your wife away. If you cooperate with this, you are essentially conveying some support for his position.
The good news is that, after a while, this situation will likely change. But this is contingent on your wife adopting a mature, resilient approach, and not developing a hostile relationship with your son. If this happens, the situation will likely not improve and will serve as a source of unhappiness to all of you.