I have been down this road.
Our previous trailer (a Rockwood) leaked through the skylight above the tub after the first rain we had it. Went up on the roof and discovered the ham-fisted guy at the factory had torqued two of the screws down so tight they had cracked the plastic. Had to call Forest River and get a replacement skylight sent to me. We lived 7 hours away from the nearest dealer so I did the work myself.
I was very surprised at just how THIN and fragile the skylight material is on those things! It is unfortunate that this has happened to yours. Don't know if yours is cracked or not, but if it is, the only way to fix it properly is to replace it.
One last thing. I had to wait almost 30 days to get my replacement skylight. It was during rainy season here in Florida so I took a couple of pieces of 2 inch Eternabond tape and covered the cracks. This kept all rain out while I waited for the replacement. I probably could have left it with the Eternabond on it and used it for years without problems to be honest. So if you don't have the time to wait for replacement, or need a temporary fix while waiting, get some of that tape.
Good luck! Whatever you do, do something quickly. It is NOT just dripping into the tub.... water is getting into the layers of the roofing material also which will lead to horrible problems pretty quick.
2005 Excursion V10 with 4.30 gears dragging a 2014 Jayco 294BHS with an Equilizer hitch!