The one working in Canada will have to pay
taxes in Canada, the one working in the US will have to pay taxes in the US. He may or may not have to declare your income on his IRS return, but it is unlikely that you'd be double taxed on your Canadian income.
Why is he applying for a green card if you and the kids are moving back to Canada? This *may* affect his application, or it may not. The purpose of applying for a green card is to settle in the US. If your husband has no ties to the US other than his job, they may question his motives.
You *may* also have difficulties visiting the US to go back and forth. With your husband in the US, they'll consider you have more ties here than Canada. What is *your* current status in the US? Anything?
I know of one Can/Am couple where the wife was Canadian and the husband American. They lived in the US for a time, and she applied for a green card (based on marriage and
K1 fiancee visa). During the processing because it was taking so long, they decided to apply for her husband to immigrate to Canada, but as that takes so long, they stayed in the US to wait it out. She went home to Canada to visit family for a short trip. Upon trying to re-enter the US, they had somehow learned of her husband's application to Canada, and they recinded her green card application and denied her entry. She was not able to even visit the US, and her husband was unable to move to Canada until his application was processed, about a year later.