Your son's behavior is entirely normal, in the sense that he is doing precisely what he has been 'taught' to do. His behavior is not at all the norm for a child of three, however. He should be falling asleep on his own, in his own bed, and remaining in his own bed throughout the night. You are absolutely correct in your thinking that this situation can be renedied by putting your foot down and insistying that he remain in his own bed. Many parents create this problematic situation unwittingly. They think they are doing the right thing, but they are mistaken. Setting this right will not in actuality be a rejection; it will be teaching your son appropriate independence for his age. In this instance your instinct are correct; your wife's instincts, while understandable, are not correct. If you don't solve this situation now you will be trying to solve it years from now.
We had a star chart (though difficult to do this around the holidays) for a toy my son really wanted. He got a star for every night he stayed in his own bed. If he came in with us, we didn't scold or punish him, just no star that night.
We often went to the toy store to "look" at the toy he coveted and was working towards, we all chattered excitedly about how great it would be when he earned enough stars to get it, and so on. There was some whining about it, but we tried to keep it positive and upbeat. We went through a LOT of star-less nights, but eventually he caught on and earned enough.
Make sure you make it "expensive" enough so he doesn't immediately revert to going back to the old ways. Another bedroom would be great--you can let him help decorate, have a party to celebrate graduating to the "big boy" room, etc. You can also work the star chart into this--so many stars til he can have his own room, etc. I bet he would be into it.
good luck!
You might consider taking your son to the store to buy bed sheets with a kids theme that he might like. They really enjoy making decisions of their own. The toy idea is great also. It worked for me. In our case, our little girl wanted a ball pit (inflatable toy with small plastic balls). She had wanted this toy forever, so we made her a deal: sleep in your bed and stay in your bed, and you can get the ball pit. Worked like a charm. We still have those occasional nights of her getting out of bed, but I always put her back. It also helps to remind them through conversation throughtout the day, what is expected of them at night. Hope this helps.