Carol is a clone of Mike
Some crazy mad scientists were working on a way to artifically create Half-Identical Twins, and they paid Jason and Maggie for permission to experiment on the newborn Mike. Maggie was employed as the human incubator for said experiment, to cover up what was goin on. The experiment worked, sort of. While Carol didn't turn out quite as identical to Mike as they hoped, she was remarkably close. Afterward, the scientists moved on, and nobody in the Seaver clan spoke of the incident ever again.- Or, being siblings they just look a lot alike.
Ed and Irma previously had an affair.
Based on the way they behaved in the episode Anniversary from Hell, I don't think it would be a stretch to assume they'd been involved in the past. Most in laws, even ones that have been related by marriage for decades, don't greet each other like old lovers. We also see Kate and Irma have a mutual dislike of each other.Mike wanted to talk about Sandy one last time.
Another installment in the story arc concerning Sandy was planned, with Mike accidentally learning that Principal DeWitt had lost his teenaged daughter to a drunk driver (in a separate crash). When Mike stumbles on this – he sees a picture of her on his desk, remarks if he can go out with her and DeWitt angrily tells him never to return to the school (before he breaks down crying in his office) – he also sees that Carol is still in deep grief over Sandy's death. Conferring with Jason, who has heard about school assemblies where drunk drivers talk about their experiences, Mike gets Carol and DeWitt to agree to come to school and talk about their personal experiences. Which they do. The assembly is a huge success and both Carol and DeWitt thank Mike for letting them talk about the people special to them and the impact bad decisions can have and to urge teens to never drink and drive.