It does sound like you have a leak using that much LP but it SOMEWHAT depends on where/when you're camping. I have used a 30 lb. bottle in as little as 4 days with the furnace running a heavy duty cycle (temps in the teens and below) but don't know the situation where you're camping or anything about how well insulated your trailer is. BOTH of those things will have a big effect on LP use of course. Since you have no LP detector going off AND smell no fumes inside I'd concentrate your leak checks on the exterior of your trailer. Doesn't usually take MUCH of a leak to set off the detector but might be a good idea to do some tests to be SURE it's working also. One easy test is to simply turn on a gas appliance (unlit and watch how long it takes to set off the alarm) but do this carefully and don't allow yourself to get interrupted :E I think I'd want to KNOW my detector was working if there is any possibility of a leak.
Good luck / Skip