The way JS kept saying "we" and seemingly inserting herself in the school drop-off reminded me of the way my partner will tell people that "we" did a bunch of things around the house all weekend until I side-eye him into admitting that I actually did it all while he slept in and had a nice rest. It is clearly untruthful but not malicious, IMO- he subconsciously realizes he should have been up and helping out and not leaving it all to me and therefore starts to say "we" did things so he doesn't have to confront the uncomfortable feelings of not pulling his weight in certain areas. IMO, that may have been what JS was feeling as the spotlight was suddenly on her and her parenting and people were questioning why she was at work and not at her daughter's party, whether she was looking after her daughter that night, why SS was taking Madeline to school instead of her, etc. Like she may have been feeling uncomfortable about how much she's been relying on SS to handle parenting tasks now that the whole world is picking apart the timeline of where she was and where her daughter was and all that.
I can't for the life of me figure out what would make her say she saw Madeline getting dressed for school at 8:00 a.m. when we know that's just not true, however.