Nope, it won't be strong enough, you need to spend $110.......just kidding :B
Here is a good informational site about trailer 12 Volt systems:
12 volt side of lifeTypically, folks buy generators to afford available power for 120V devices and to use their onboard converter to recharge the battery. If an Air Conditioner is part of the plan, you will need a fairly robust (3000W) generator. If you are just charging the battery back to a 90% State Of Charge, a smaller 1000W generator will get you by. If using the generator in a campground setting, an inverter-generator is what you need because they are less noisy and comply with Park and Forest regulations.
If you're using your battery, continually, until the lights no longer illuminate and charging to some unknown State Of Charge, you will be buying many batteries. You really need some type of meter in the system to know what is happening with your battery and to measure the SOC. This can be as simple as a plug-in meter in a DC cigar lighter receptacle or as thorough as a battery monitor like the Trimetric or Victron.