There are several compounds that remove heavy oxidation from gelcoat but the easiest I've used by far is to start by wet-sanding with fine abrasive paper then progress up through the compounding phases to pure polish then wax.
The problem with gelcoat is that it will really clog up the compounding bonnet pretty quickly if heavily oxidized.
I've even used comet and ajax as a first step to get the really heavy oxidation off before starting the compounding phases on desert boats. That works really well on deck where you can sprinkle it on heavy but be extra careful around aluminum, port windows, hatches etc.
Have you seen Mainsail's post on polishing and waxing? It's worth a look.