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What is the model number of your fridge? It will be on the inside of the box and begins with an "RM" and some numbers. I am going to offer you the phone chat option in case you think it would be more helpful here.
Go to the link below and you can grab the Dometic Service Manual which covers this model. Print out a copy or at least Bookmark it so you can come back again later to it. Lots of good information in there. http://www.fourwheelcampers.com/NewDometicRefrigeratorManual.pdf
Is the fridge level? Do you notice any difference in the temp from AC mode to LP mode? How long has it been on and how long since you used this last?
This may be a thermistor issue IF the cooling is about the same on both modes. You can test for this in just a few minutes. Having a small digital multimeter like you can find at most hardware stores is helpful here.
Poor cooling on LP mode is USUALLY the result of low LP gas pressure at the tank regulator. This needs to be checked and adjusted at least once a year.
One way to tell sometimes if the LP pressure is too low is to turn on the large burner on high and see if there is any yellow or orange in the flame tips. That can indicate low pressure.
You are welcome.............perhaps they didn't check this before it was delivered.