If me and my SO were waiting out to pass our one year mark of living together to apply for common-law and decided to go back to Mexico to wait out the remaining period of 3-4 months, where I (Canadian) would not be working, would I need to send proof in our application that I will to reestablish myself in Canada? As in have a job to support us?
If you are only in Mexico for 3 or 4 months as a visitor, you can claim you are just there temporarily and are actually resident in Canada. So you won't have to provide proof of your intent to settle in Canada. If you go back to Canada just before you send the application in, so you can legitimately show you are back, then the visa officer should have no questions about it.