My advice--just for consideration--not telling you what to do...
You need to have an adult commitment to your wife--and to have a relationship with your son, he is going to have to have one too--with you and with your wife. That means he should be able to accept talking honestly with either of you (not just "both") and not just about how he feels but about the damage he does by his actions. If he can't do that, then meet him in a coffee shop or spend time in some neutral place with him if he just needs to talk.
There can be no "sides" in a family and everyone has to work for everyone else's good--not demand that others be sacrificed for their good. If someone can't do this, then they're more a tenant than a family member.
I think your wife's actions are essentially saying, "I can't handle the stress and it hurts me--please don't put me at risk again.". If your son can't be an adult (and he already broke trust before) then you put all of your relationships at risk bringing him back with no willing boundaries--meaning he has to really accept them too.
Let your son know you love him but that you won't sacrifice another family member if he can't work out his own responsibilities in his own life first.
I have a son who did the same thing and I sent him away with enough money to make it for half a year. Then I kept the door locked. It took two years for him to get to the point where he started to understand that to be welcome, he had to change for us--not us for him. Now we get on great--but it was a nightmare getting there. His behavior really impacted my wife, myself and his two younger brothers and years later we are still dealing with the after effects.
My middle son lived out of state and entered a fast relationship with someone who was not very responsible (they're much better now). He announced one day, "I'm coming back and we'll stay with you for a month or so until I find work"...he has a new baby and two step-children. I told him, "No". It would have not worked--the same stress your wife seems worried over was an issue with his situation.
His wife (they are actually just getting marries) only spoke polite hello's to me for the first two months but when she saw we were on her side she started being more open and honest. A month back she told me she was intimidated by me at first but decided she liked the fact that I was always up front with her and she knew exactly what I meant. We get on great now and she calls me "Dad". Go figure.
It isn't easy--and it can seem hopeless when you are in it. All you can do is the best you are able and know how--and what you think is best for everyone. The rest is on them. They can get mad or they can make it better--their choice and not your responsibility or place to make it for them.
Sorry you have to be in the midst of this--I know its no fun.
I think Philly has a fair perspective on this but just because a couple of years have passed is no guarantee of "he's matured". It has to be demonstrated. I don't believe in "absolutes" here. A couple of years after my son moved out, his whole world fell apart and I went and got him. I let him stay three months with us to hget a job and get back on his feet and told him it was zero-tolerance...if he told someone he was "going to kill himself", if he stole anything or screamed obscenities or flew into rages he'd be out the first time it happened. I specifically made sure he knew, "Here's what you can't do while you're here--no matter what's going on in your life."
As a last note, if your son is hurt by not having freedom to stay--explain to him that his relationship with you is a given but that he's going to have to create one with your wife himself if he expects one with her. That's up to him--not you.