We did not eat at Ohana, but did eat at Kona for dinner. Our kids have allergies to all nuts.
As you know cross contamination is an issue at any restaurant, anywhere, regardless of whether they serve peanut sauce or not.
To give you my long term perspective: From my experience with other parents in our school district, I think my wife and I are on the extreme caution side of things in relation to many other people.
For example, we don’t eat any ice cream in our house made by companies, as they all will tell you they use shared lines if you call their support phones. We have several friends in the district who do allow their kids to eat various brands, citing the manufacturers’ statements that they make vanilla first, other flavors next, then clean the machines before starting over. However, we’re not comfortable with that since there’s no info on how they clean, whether they test for nuts after, or how they test if they do.
Back to Disney: From my understanding after our talking to several chefs on our 2 trips, each kitchen has a dedicated zone for food preparation for the common allergens. They will also go out of their way to inform you of any outside sourced items that may have cross contamination issues. (BOG was one of the few places we ate at, for example, that had cupcakes made in-house and no known cross contamination issues.)
With the service and help we’ve had at Disney, I think my wife and I would be comfortable eating at Ohana. But, we would be sure to not only get the lowdown from the chef, but that the waiter completely understands. (Waiters often seem to forget that salad toppings are issues and then put them on without thinking even after we’ve talked about allergies.)
Also, we’d ask that they clean the table with fresh cloths before our kids sat down, and we’d break out our own wipes for the chairs.
If it makes sense, we try to be as cautious as possible with what we eat, but also try to get the kids to understand what they’re going to have to do in this sort of situation, probably for the rest of their lives. Our daughter is on the over-cautious side, our son: not so much and makes us nervous as he enters his teen years.
Of course, if we find we are really going to stress over the decision (as we sometimes do) we’d probably end up staying away rather than lessen the vacation experience.
Here’s an older thread on another board that has some discussion as well.
Hope you have a great time everywhere you eat!