Hi. Up until the middle of January, I was a Cast Member at The Spirit of Aloha Dinner Show, and I can tell you that we do take food allergies very seriously. The pea allergy really shouldn't be a problem as we don't use peas in any of the recipes (though we do use other legumes); we also don't use peanuts, other than in pb&j sandwiches for picky eaters (though we do use other treenuts). My advice to you, if you decide to go, would be to call a few days in advance (or more) to let the restaurant know about your food allergy concerns as there would be more options available to you than if you let a cast member know when you are checking in that night for the meal. Either way, one of the chefs (most likely Chef Eugene or Steven) will come out and talk to you before your meal, and your server will also be very much aware of your allergy as well so as to try to make your meal go as smoothly and enjoyably as possible. I can also tell you that somewhat recently (around November) the luau changed a lot of their allergy options so as to give better options for the guests.
Somewhat on a side note, if you do decide to go to the luau, please stay through the third act when all of the traditional Polynesian dances are performed (it's the longest and also, imo, the best act); some guests give up on the show after the first act (a short introduction to the characters and the frame story) and the second act (audience participation)---trust me the third act and, in particular, the Fire knife dancer are really a lot of fun! Hope this helped a bit