I would NOT let him move in until this is settled. His son does not get his own room, he can sleep on the couch when he stays overnight.

You need to delay the move in. You and SO are not on the same page when it comes to his kid and perhaps other things as well. You said he was being critical after looking through the rooms of your boys - which he shouldn't have been doing in the first place! How long have you been dating?

Are you sure you want to marry this man?  Some of his behaviour sounds like it is on the knob head spectrum. 

Nope, this guy has no concept of appropriate behavior or limits in your home.  He has way over stepped and he hasn't even moved in yet.

I would stop his moving in immediately. You nor your sons need this man or his odd spawn infecting  your lives and home.

Keep in mind that his odd spawn will never be out of the picture even when he has launched and even after  your son's have launched.  All of you will still be stuck with this man and his son.... for the duration of this relationship.

Do you really want that for yourself and your boys?

IMHO of course.

In my first marriage my XW made no effort to integrate into my family while she and her parents fully expected me to integrate into their family to the point of marginalizing my own family.  When that marriage blessedly came to an end I swore I would never again allow anyone or anything to marginalize me from my family.

My incredible bride of 26+ years is the daughter my parents never had.  She is all in as a family member and in many ways is closer to my family than her own. Though I make sure to keep her in contact with her family and push her to visit them regularly. I visit with her family every 3rd or so of her trips home.  I would not do to her what my X and her family attempted to do with me.

Interestingly my brother has taken a far different approach with his relationship with mom and dad and my family. He pretty much makes nearly no effort.  I have confronted him on it and he gets very defensive.  He is of the perspective that he is doing what mom and dad did with their family.  We always lived on the other side of the planet from both my dad's family and my mom's family.  We visited both sides of the family at least once a year.  My brothers interpretation is that he and his wife are doing what our parents did.  For some reason he is incapable of progressing his childhood family experience to a broader actively participatory family model.  

I finally reached the end of my willingness to visit him and his family. So, I just stopped.  I stopped visiting, I stopped calling, I just stopped.   It took a few years but eventually he gained a clue and called me to ask why I had stopped visiting and calling. I just told him.  He has never made an effort to visit me or even to call so from now on the relationship was entirely on him.  I missed him, I love him but I was no longer willing to serve myself up to heartbreak and disappointment.   So, now I answer his calls when he makes them and I have even traveled long distances to help him with things he needs help with.  But... I do not chase him around begging for relationship crumbs like I used to.  He and his family have lived internationally for many years. My wife and I have as well.  We repeatedly invited him and his family to visit us in the places where he and I had grown up together. There was always some bullshit excuse for why that never happened but there was a sure expectation that we visit them.

Interestingly.... just a week ago my DW and I visited my parents and spent a week RVing with them an hour and a half N of my brother's US home.  I had no intent nor any desire to visit my brother and his family.  I have been at an end of my rope point for a while now.  Surprisingly.... my brother called me and outlined their plans for the last month of their US based summer before returning overseas.  They will put my youngest nephew in university on the 14th then head S to visit with my SIL's parents and then..... they intend to come to our home.  I was speechless.  This is the first time in more than 20 years that he has even given lip service to making an effort to visit.  I was at the point where I was ready to give him both barrels in venting my pain and hurt with his historic crap.  My DW begged me to hold my tongue and not openly confront my brother.   I had decided that I was no longer willing to let the hurt and pain go unspoken.... then out of blue.... "Hey, we are planning on visiting you in 4 weeks. Would that be okay?".  I was speechless for several moments.  He knows he does not need an invitation.  My wife and I have always made that clear.   I am glad he made that call before I let loose.

Now... will he actually visit?  I hope he does.  For now, just making the call to tell me he intends to visit is a huge deal.  My brother is my life long BFF. We have always been extremely close even when he was making no effort.  He would call occasionally to ask my opinion on some problem or another.  He and I are 6 years apart but were about the only people we each had to have adventures with for many years of our childhood. Those unique experiences created a closeness that is not common between sibs with the age difference that we have.  This is probably why adjusting to our adult relationship has been difficult for me.

Okay, time shred another copy of my man card.

Don't let either of them move in until you're satisfied with the situation 

Break it off. Your fiance has no respect for you or your home. Checking out your closets? Saying your sons can room together when his son comes over? WTH! He sounds like a user. At least you know now before you tie the knot.

This man has no respect for you and your home.  Trying to move your kids into one room so SSgetd his own room.  This kid will never leave.  Do you really need this type of relationship?  You already know it's not going to end well. Before it really started 

why was his power off? You screwed yourself completely. First you cant let someone move into your place and call it home, then complain that they are making it a home. You also need to seriously think about his other kid. You already believe something is different with him, so you need to understand there is a chance he will be living there.