Unfortunately, there isn't a easy way to remove paint. You could try using a stiff wide putty knife to lift or scrape it off. Also, it is possible that simple very warm water could help loosen it from the bottom layer.
It is strange that this layer is having problems. The good part is that any paint that won't come off can actually stay. Do your best to remove the loose and peeling paint, then prime the affected areas with a quick drying oil based primer. Now some drywall mud or spackling paste can be applied over any ugly paint edges, sanded smooth, spot primed then painted.