It could be the regulator. There needs to be a certain LP pressure to the stove as well as the refrigerator
A couple of years ago my fridge would light
but not heat enough to cool for food. The stove worked fine. I stopped at an RV shop and the first thing he did was check the pressure at the stove and fridge. It was low. He replaced the regulator and all worked well.
One thing he told me was that the regulator was mounted incorrectly. It was mounted with the opening facing to the rear when it should be facing downward consequently it likely gathered more dust and dirt into it.