Infidelity Support Group
Any relationship in which one partner engages willfully in sexual relations with another outside of the partnership is considered to have experienced infidelity. This breach of trust is often traumatizing for the faithful partner as well as the relationship, and support is often needed to heal emotionally and to decide whether or not the relationship should continue after...
As long as you have access to his digital devices, including his phone, and email accounts, there's no reason you can't keep tabs on his activities until you feel safe enough to build some trust. Also, where does he go that you feel the need to keep tabs on him? Isn't he coming to your home after work, or calling you to go out for dinner, or better yet, inviting you over to his place to cook you dinner? Let him prove to you physically, that he's changed. Words are cheap, and so is holding hands, and going to the movies. This doesn't show he's changed, this just shows he knows what to do to please you, and there's a huge difference, and I think you're being fooled by his simple actions.
If you've been apart for a year, you need to handle this as if you were starting anew, and dating seriously. Most seriously dating couples end up living together practically, where they spend most or all of their free time at one another's place. I think this would be ideal, and probably your best chance at seeing if he walks the talk, before investing in living together. You're doing this because you're afraid he'll stray if he's not under your roof, and that's the worst reason to take someone back into your home and into your life.
But yeah, give him time to see if he walks the talk, bringing him under your roof now would probably be picking up right where you left off. And if he's sincere, he WILL be there in 6 months, in a year, no? If he really loves you and wants you, he will wait. I would also expect him to have identified what made him cheat and what he will do should those triggers present themselves to him again.