My son has a peanut allergy and we will not have dinner there if he is at Disney. My daughter and I have eaten there and the peanut sauce is everywhere and the chance of cross contamination is high.
Even when all of us have breakfast there we make sure to wipe down the table and his chair although no peanuts are served in the morning. (And I hate to say it but the chairs in particular have been very sticky and dirty with a substance that could very well be peanut sauce.) I think it is too risky to chance it if his allergy is severe as most peanut allergies tend to be.
If he has a tree nut allergy, that is a different story. I do not believe that tree nuts are used at 'Ohana dinner. Peanuts are not actually a nut, they are a legume.