You are setting yourself up for a world of pain, OP. Kids NEED boundaries and consequences. The less you assert boundaries, the more dysregulated your toddler will become. It’s a vicious cycle. Car seat is non-negotiable.
Set up the situation with appropriate transitions then:
Request
Reminder
Consequence
Example -
Set up might me a 2 then 1 minute count down, “DC! In one minute we are leaving your books and getting in the car.”
Request, which can be an invitation to play. “DC! It’s time to get in the car seat please. Would you like to walk, or fly like a plane to get in your car seat? Wheeee!”
Reminder if they refuse/ignore, with information about consequence “DC! Listening ears! It’s time to get in the car seat. If you don’t walk, I will pick you up and put you in it”
Consequence - pick them up and force (safely) them in. Do NOT stop the consequence when they protest and start complying with the request, it’s too late and you have to follow through or they won’t learn to do it first time. “You didn’t walk when I told you to so I am picking you up to put you in the car seat. Let’s try again next time to have listening ears and do what mummy says.”