Shakyjay is spot on with his assessment of my situation and wants.
That said, I may just spend the money and get the inverter installed in the trailer to power all outlets. Seems it might be worth it.
In regards to a few of the TVs mentioned, many of them say 12v, but I emailed Insignia and they sent me the following:
"Hi Stephen, (which isn't my name, not sure where he got that from. Haha)
This is Sal with Insignia Products. I'm writing in response to your inquiry regarding regarding the power requirements of your TV 20ED310NA15. I will gladly provide you with the most accurate information
After going over the specs of your TV, I can tell you with confidence that it has been designed to work only with a 12 volts AC power adapter. The reason why you see "DC 12V 3A" on the specs, is that it refers to no more that the power requirements and not an actual power cord. If you no longer have the original adapter, Insignia has one that can be purchased at any BBY Store."
So anyway, to simplify things, I believe wiring in the inverter and buying whichever TV/DVD combo I think is the best quality for my price range will be easiest. In the long run, it will be nice to just be able to plug most things in and have them work. It will benefit me more in the long run to have the inverter.
Thanks to all who responded. It helped steer me in a better direction. Much appreciated