The skylight turning hazy is due to UV exposure. Eventually the sun will take a toll on the skylight just like it does on the ceiling vent covers. You'll need to try something you can put on it to protect it from UV and plan on replacing it in the future as preventive maintenance. Inspect it from time to time and look for cracking around the edge of the inside edge of the flange. When replacing it they make skylights out of UV resistant plastic but they will be a little more expensive. Figure on replacing it after the trailer is about 6 years old.
Mine turned hazy and also developed cracks after about 7 years at the inside edge of the flange where the plastic curves to form the flange. I had noticed the bottom lens had condensation on the inside and when I took it down water had been running under the ceiling paneling. That's when I saw the cracks in the skylight. the Skylight framing was damp and water stained. I could see that water was wicking under the ceiling paneling. When checking the ceiling panel to see how sturdy it was I wound up putting my thumb through a spot where the it was rotting. There was some wet insulation and signs of beginning of rot of the rafters in the ceiling. To stop any further water from getting into the ceiling I packed some small pieces of paper towel under the edges of rubber roof that was folded down and stapled inside the Skylight frame to make drip edges so the water would drip into the tub and not wick into the roof anymore. I'm going to get some clear Flex Seal to spray the entire skylight on the outside of the trailer to seal it so it doesn't leak anymore. Then when I get some time I'll have to remove the metal edging along the roof edge so that I can lift up the rubber roof and see how bad it is, take care of any damage and replace the skylight. Due to the age of the trailer I might as well replace the rubber roof anyway.