When I say "reinforce," here is an example of what I mean. (I'm not looking inside your particular door, so this is more general.)
1) Separate inside and outside of door, so you have two fiberglass skins (or, alternatively, cut a large opening in the inside skin, if it is going to be covered by carpet or etc. anyway).
2) Patch outside door skin from the back (inside) with fiberglass cloth and epoxy resin.
3) "Reinforce" outside door skin from the back (inside) with something such as more layers of fiberglass, or a piece of pre-made fiberglass board (say, 1/4" to 3/8" thick and 8" x 14", for example).
4) Put door back together
5) Repair gelcoat on outside of door.
6) Remount holder-opener hardware, running fasteners through new reinforcing block
Note that depending on strength of door and hardware mounting, it may go through both door skins. In this case you would want the reinforcing block to fill the space between the skins (thickened epoxy, for example) and then the fasteners would go all the way through.