If you offer them accommodations you do not have to separate them.
Many people choose to have this as a house rule, but in your situation of a spouse who has a differing view it is unlikely that this will be a house rule in your home.
You are not committing any sin. You’ve offered them a bed, what they do is not your issue. Even if in different beds, they could still easily rendezvous for hanky panky if they wanted to.