Either buy the ticket to your destination or buy a seat for your child so you don't have to check the car seat.

You're trying to have it both ways here, and a lot could go wrong likely over a small amount of money. If your car seat gets gate-checked and goes to IND, will the savings from doing the hidden city option be worth it to you?

Do yourself a favor and don't try to thread the needle on this one. I'm all in favor of saving money by being smart, but I think you're outsmarting yourself here.