Your problem is complicated by the poor fit. Are the milky portions on the outward facing bubbles in the clear?
I can't tell from the picture what the source of the whiteness is. However, we have had clears go milky on us when it has been raining for a while (days, not just a few hrs.). The other thing that happens to dodger
windows is UV damage, and the plastic goes opaque, not really milky. It also become "dry" and stiff as the plasticizers evaporate. Skin oils can make it go milky, too. In general, just wash with dishwashing detergent, and it will remove dirt. You may need a good quality plastic cleaner. There are different ones available, both cleaners (which will remove stubborn oils) and polishes, which will smooth out the surfaces a bit.
If you want to fix the dodger, it can be done, but it will be a fussy job because you'll need to alter both the "window" and its surround. If you're up for it, it might even be worthwhile to start afresh. (!) Watch the SailRite
videos and read the directions, and proceed. Actually, do that either way. Then if you want to have a go at fixing it, send me a PM.