Hi Pg, I have recently discovered that rust can be removed from fabric by squeezing lemon juice on the rust marks and then leave out in the sun! You could try that on your cooler, if not, I gather o alic acid will remove rust stains, but I would try a small amount in an inconspicuous place first - just in case it melts the plastic, though I don't imagine it would. Good luck
I would try some Bar Keeper's Friend and a green abrasive pad.
Thank you. I have that product, and will try it.