If you could provide a picture of what your screen looks like it would help trying to figure out what is wrong. At 12 years old the screen frame could be bent, out of square etc. or it could be something in the framing of the trailer wall. There are all kinds of "sealer" tape/foam that might help but if you can assess the root cause and fix that, it is the better solution.
As far as ants, when I have an issue with them I spray Ortho Home Defense. I carry a gallon jug with the little hose and battery operated handle. I spray the tires inside and out along with the tongue jack to keep them from migrating up and into the trailer. I then spray the ground around the trailer front and back to stop them from irritating me. Depending on how bad they are and the weather you might have to repeat the procedure every 4 weeks or so.
As far as mosquitos repairing the screen frame should eliminate them from the inside unless there are other openings or you go in and out the door a lot. There is another thread about "mosquitos" that you might review that discusses alternatives to repelling them outside.
Danny & Susan wife of 53 years
2019 Ram 3500 Laramie CC SB 6.4 4x4 4.10
2020 Montana High Country 331RL