If a child seems to be in charge, that's not a good thing. That would be the child, represented by my left hand up on top, and you down here.
Even though it seems like children want to be in charge and it seems like they want to call the shots, they don't. It's very disconcerting for a child to feel like they are on a ship with no captain. You want to get back in charge, be the one guiding the ship. If the child digs in their heels and says, "I'm not going to school. You can't make me." Don't come across as panicked or desperate or needy. Don't say things that will imply that you absolutely have to get them to school and you'll fall apart otherwise. It disempowers you and it reinforces the child's sense of being in charge.
Don't issue threats and bribes. Just say, "You know, honey, I get it. It would be nice to stay home. It's such a cozy time. I see. I understand." You want to, kind of, bring everything down. The main thing is don't get involved in the push. Don't get engage in the power struggle. Don't react to the threat that they are making or the stand that they are taking. Simply acknowledge their point of view, stay calm, and in charge.