First, I would not hide his aunt's condition and up coming death from your son. He needs to know and will be even more upset if it comes on him suddenly without warning, and with the knowledge that it was kept from him.
Second, as to whether he is included in the funeral. That depends partly on how he behaves at family functions. If he does okay at functions, then let the choice be up to him. However, do explain to him ahead of time what will happen at the funeral.--The service, the visit to the graveside, the lowering of the casket and people laying flowers on the casket, etc., followed by a gathering at a hall or at someone's home. At 13 he should be able to handle the funeral, if he is able to behave at family functions, as long as he knows what to expect.
I've been to a number of family funerals over the years, including my mother's almost nine years ago. Yes, it is hard, but it happens to everyone eventually. Just remind your son of that, and that it is a perfectly normal part of life, so he doesn't get too fretful about it.
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If a man does not keep pace with his companions, perhaps it is because he hears a different drummer.
Let him step to the music which he hears, however measured, or far away.--Henry David Thoreau