KS, if your refrigerator is like ours, we have observed the same problem.
The issue is that Dometic's flex handle design isn't really very good. I doesn't provide for a positive latch close.
But... I found a very simple solution. I insert a short piece of soft rubber tubing between the handles before we head out. They stay put and ensure the doors don't come open.
Here is a picture of what it looks like with the rubber tubes inserted:
Tina + Dutch and Bell, Bobo, Harley, Buddy (the dogs)
2011 F350 Lariat 4x4 DRW SuperCrew 6.7L (B&W setup w/Air Lift 5000 Ultimate)
2014 Columbus 365RL (Airflex and Voyager package)
Nights Camped 2014 - 154
, 2015 - 32, 2016 - 4