Him going sideways meant his braking wasn't working. If there's slipping you want to let off the brake and down shift (you can do this in automatics) to the lowest gear that doesn't make you slip. Staying straight to where your wheels aren't slipping is a priority over braking or getting slower. The only way of slowing is to have traction, and you don't want it while sideways.

I would have tried keeping straight and then veered over into the dry lane and started slowing down.