Not sure your AC could keep up if you are blowing all your cooled air out anyway, hot air would have to come through the cracks to replace the cold air you are blowing out.
Yes, the oven is meant to exhaust behind the stove and the stove to be exhausted out the hood vent. Somewhere manufacturers lost their way.
If you cook a lot then it would be good to add a vent hood that blows outside so the trailer does not smell like food, or that grease does not stick to every surface inside.
Easy to just not use the oven except for sock storage when it is hot.
Sorry, camping involves some compromise.