If I remember correctly, from past reading, the Trillum hinges are screwed into a wooden member that is under the Ensolite on the inside (you should see a bulge there).
The gelcoat cracks are probably caused by some sort of stress, which is often concentrated at fasteners. Especially if there is movement.
The hinge screws may have worked loose over time, and/or the wooden backing piece may have become soft through moisture or rot, and then no longer held the screws properly.
Assuming the set up is as I'm remembering it, I think I would go in with the following plan (of course potentially modifying it as you find out what is actually happening).
1) I would remove the hinges from the trailer
2) If the wooden member is not rotted overall but in the screw hole area only, then I would overdrill the fastener holes (make them, oh, say, 3/4" with a hole saw), and then fill the holes with thickened epoxy and let that cure (be tidy with tape and etc.)
3) Then, after checking on fastener size, I would re-drill the proper sized hole to accomodate the new fasteners. This should be centered on the epoxy plug, and leave an epoxy annulus around the perimeter. Of course make sure the door is lined up properly and the holes lined up with the hinge.
4) Note that I would most likely go back in with machine screws (i.e. fasteners that are non-pointed and have a nut on the inside), but you can probably use screws if you are really set on not having nuts on the inside. Note that if you use machine screws, and you want to be really anal, you can "tap" the fiberglass plugs, but that is not necessary.
5) Now, while you have the hinge off, you can repair the gelcoat cracks. I feel like I may have written the steps for that up here before; or, someone else has. In short you prep, route, and fill with gelcoat to slightly proud; then sand down to flush and sand progressively finer until glossy (1000 grit or so). Note that you will want to "buff out" (compound or wet sand) the surrounding gelcoat first so that you are matching "healthy" gelcoat and not oxidized gelcoat (lighter in color).
6) The Silicone. Ugh! But, if it is just in one screw hole, and you use a hole saw to overdrill it, maybe that problem will go away
7) When you re-mount the door, use a good bedding compound such as butyl or polyurethane caulk (or other suitable type).
I hope I haven't forgotten any steps, but this should give you a general idea, and feel free to PM or ask questions here
Note that you will want to prep the gelcoat by removing any mold release wax, before you do any sanding or etc. Interlux 202 is one product that works, but there are others. The main thing is to use a lot of disposable towels or etc. and not to "re-wipe" with the same part of a towel, because that will recontaminate the area.
PS: Okay, here come the PS'es
One you start to remove the damaged gelcoat, you can see if there is any underlying fiberglass damage, and repair it at that time.