""Mom" going to Hell bugged me because doesn't Luci still have a deal to bring her back to Hell that he hadn't quite fulfilled his end of yet but was also sticking with the technicality that he could/would do it but didn't yet?""
No one really knows what Dad wants, and what Lucifer agreed to was to "be the son You want, go where You want." He just assumed that the open door meant he was supposed to track Mum down. It could just as easily have been Dad saying, "See? I forgave your Mom, too, and set her free."