You're thinking way to small.
Of course you're not going to run heating appliances off solar power - even stored solar power. Ditto air conditioning. But a trailer has a lot of loads, and they're usually not all that efficient. You get maybe 5 solar hours (hour of noon-equivalent light) per day, so a 15 watt panel will give you about 5 amp-hours of charging. That's enough to run one light bulb for four hours.
Your battery might leak that much power in a day. A 15-watt panel is good mainly for keeping your battery charged when the trailer is parked in storage.
You'll have a LOT of loads in a trailer: Propane detector. Motors in a propane furnace. Modern propane fridges have a computer and a selonoid to turn on the gas, and just the selenoid pulls more than an amp. Vent fan for the bathroom. Stock lighting is, of course, incandescent.
My self-contained camping trailer had a couple 95 amphour batteries and they were good for no more than two nights if it was a heating season. It was designed to be charged as it was towed, and plugged in at night except in back country. So an overnight or weekend's camping was all the manufacturer had in mind for power storage, despite fresh and waste water storage good for at least a week. And we bought it off the lot so it didn't come with the optional hookup for rooftop solar panels.
So you're going to want at least 200 watts of panels, and 400 would be better, if you aren't going to have a power hookup or run a genny and have loads like mine had.
If you're on a windy site (and not too close to neighbors) you might consider a small windmill, like our correspondent from Alaska uses. Either instead or (better yet) combined with solar. In many climates it's windy when not sunny and vice-versa.