Pretty sure that pine nuts are actually seeds-- from a very particular species of pine, in fact.
At any rate, what matters more than whether or not something is technically a nut is what it seems to be most highly correlated with.
Some nuts correlate with allergenicity among a handful of them (pecans, walnuts) and some not (walnuts, cashews).
Sometimes those groupings make sense on the basis of biological relatives (like in my example) and sometimes not.
For example, there is NO reason why so many people with peanut allergies should be also egg allergic. Or, for that matter, tree-but allergic. After all, in the one case this is a legume seed protein, and in the other... a protein that isn't even concievably related biologically because the two organisms are so far from one another. It's very puzzling.
But there's a very high correlation. More children with PA are actually *egg* allergic than are treenut allergic, apparently. Odd, I know.
I offered that preface to say:
I would probably be VERY wary if you have two kids who are allergic to such a wide variety of tree nuts. The liklihood of sensitization with exposure seems VERY high in your particular circumstances in light of that. Much more risk than someone who is only PA, or only allergic to, say, a single treenut.