The best way to start over and make sure not only is all of the coating removed but also the gel-coat is prepped for a coating would be to re-compound or re-polish the gel-coat.
I'd use the Captain's One-Step Compound & Polish with a foam cutting pad on a FLEX 3401 as this will remove the coating, remove any other defects and leave the surface with a high gloss finish. Then chemically strip to remove the polishing oils and then coat.