Your 7W solar panel will neither charge your battery nor supply any power for your appliances. Sorry, it's a waste of money.
You need to total your electrical loads (watts) and then figure out how large a battery that requires.
For example, my LED lighting totals 19 W, and my fan consumes about 3 watts for a total of 21 watts. At 12 VDC, that's ~2A. Which means that if I run everything for 6 hours, I've used 12 AH from my battery
Common wisdom is that you should not draw more than 1/2 your battery capacity. So my 60 AH battery should power everything for two or three 6-hour days (30 AH / 12 AH).
Your 1000W inverter will draw about 84 A from the 12 VDC supply. That means that to run it for 3 hours will require ~250 AH of battery power and require 500 AH of total battery capacity. And I don't want to know how much that'll weigh
Your 7 watt panel will replace that 1000 watts in 6 days, if it runs 24 hours a day (an impossibility with solar!).
Unfortunately inverters are total power hogs and should be avoided at all cost. If you really need 1000W of 120 VAC in your trailer, get a good Honda 2000i generator and make it easy on yourself.
<Chas>