It's easy as pie to cancel and rebook on Southwest. Log into your account and click the appropriate button: "change flight" or "cancel flight." The website will walk you through it. I would think, in this case, you'd have to cancel your existing reservation and make new ones to be considered as a new purchase for the additional RR points.
However... a couple of things to consider. First, is the fare you paid yesterday still available for today, or has it gone up? If you cancel and rebook, you'll pay the new fare. Sometimes I check this by checking the travel dates I am interested in and clicking the toggle for 8 adults. I figure, if they have that fare available for at least 8 people, it'll stand up to the time it takes for me to make my new reservation. You might also want to cancel and rebook the flights separately; yours first, then your spouse's, just to make sure you can get at least one of the tickets at your existing fare (does this make sense?).
Also... did you book with rewards points or cash? If it's with points, it's absolutely no problem; they will put the points back into your account and even hold the $10 you paid in security fees to apply to another reservation. If you paid in cash, there's a caveat: They will make the changes and put the cash in an account for you, but you need to book/use that cash within a year of the date you made the original reservation. It doesn't sound like it'll be an issue for you (based on the date you made the reservation and your discussion of getting more points) but I just wanted to mention this for accuracy/completeness.