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This was a topic I had researched some time ago for another purpose. Basically, the game cameras don't have enough resolution for the most part, to use in prosecution, if that is your aim, so I'd test first and ask that kind of question of the manufacturer.
There are several products that pop up in the RV security space that would probably help, but be prepared to spend a little coin - about half a good sized Mac Book Pro or so. I'm currently evaluating a solution in this market that says it can send videos from each camera and conserves battery by only turning on the cameras when someone is in range of a motion sensor. You may way to search for RV security systems and look for those with 3g or similar capability. There are only a couple.
If you are handy with electronics, you can get an arduino board that has support for 3g, cameras, and what not, but that would require development time - again cost.
You can also get some units out of china similar to the game cameras that have support for cellular, but personally, I'm not that brave.