S.M.
I would get a used carseat, cheap. And use it only for timeouts. Strap her in and leave her there for 2 min when she misbehaves. When she is in timeout, she has already misbehaved and to try and teach her to listen and sit still while she is in timeout is too much for a 2 yr old. You are just trying to correct her for the initial wrong. You can teach her to listen to you more effectively when she is not already upset about being in timeout.