My opinion is clear, even if the guy wasn't a parolee I would say no. It's your house, you've worked for it, so why should someone else be allowed to come live with you. My house is my domain, we have few friends come over and have few visitors, it's my place where I can go and have peace and quiet. 1300 square feet isn't very big and when you're already 4 in there, adding a 5th to the mix just removes that much more space. And that he is a parolee, I would never let anyone who has done hard time stay with me, much less if we had kids. In fact, that her parents don't want him living there as it re-introduces him to his friends and surroundings, isn't that a HUGE red flag? I read that and it's clear that his parents don't trust him to not re-offend if he gets close to the same group of people. Well you know what, nothing says there aren't 100x more groups just like them living in your area.
That aside, I feel sorry for you... this could very well end your marriage and even if it does not, it will probably put a big wedge between you and your wife/her family. It's a real shame that she is trying to take this huge (and potentially disastrous) decision without respecting your opinion.