Welcome to FT.
Unfortunately, for your sake, the rule is pretty straight forward:
The Companion Pass is valid for free travel only when the Companion is accompanied on his/her flight(s) by the Rapid Rewards Member.
If your Companion spouse cannot return on the flight(s) you are on the next day and will, in fact, travel the day before you, you will have to buy a ticket, or use a RR ticket if you have one and space is available; the Companion can only travel free when on the same flight you are on.
Except possibly for a voluntary bump situation, I don't believe anyone on FT has reported success in having the Companion fly on a different flight than the CP holder is on.