Here's two choices you have right now. Your three year old is at a stage where he wants to control his world. You just give in and let him control the little things, like who puts him in his car seat, or take the fun out of the control thing and realize that if he is going to give you a hard time about something, you might as well do it. Remember the phrase, pick your battles. Are they banging heads because they are too much alike? You can gently say "remember who is the adult" or" you like it when I do things for you too." I wouldn't call it "giving in". You do what makes your life a little easier sometimes. Is it worth the fight?
Also I've noticed that men have a little bit of a harder time adjusting to being parents. Men seem to define themselves by their job, not their parental status like we do. I think you will find that when you have your second, they get much more into it, just because they have to , and it is no longer unfamiliar ground to them. It took mine till the second to "get it" about being a parent. It's kinda like when you have one, and a SAHM, they don't have to change much about their lives. 2 kids means you are really a parent and you'll find they are much more active. I remember taking my first out to practice basketball, and baseball (although I know next to nothing about either sport) while my husband chilled out from his 'rough day' in front of the tv, which used to irk me to high heaven. Now he plays with them constantly and its second nature. ANd the worst part is, my oldest doesn't remember mommy playing basketball with him!!!!! Arg!
All kids are mommy centered. We are there most of the time. Relax in your "making" him give daddy a hug. It kinda sounds as if there are some control issues going on
with the whole household. And believe me, I was the same way with my first. I am giving advice from the experience of hindsight, not always first hand knowledge. But it's like I say to my kids, I want you to learn from my mistakes, not repeat them. So we used to do this, I would go up and give my husband a hug, and say "don't give daddy a hug; he doesn't want one". Almost every time my kids (and yes this happened with more than one child) came flying over to do something they weren't supposed to do. And my husband got a hug, Its not about the hug; its more about their controlling their world.
Good luck, girl!!