Hello Excelsior A125. Since you already play Destiny Rise of Iron on the Xbox One, that means you have already gone through the Character Migration process. Your Xbox One and Xbox 360 character progress is now split into 2 separate characters. Anything you do on the Xbox 360 will not affect your Xbox One character and vise versa (playing on Xbox One won't affect Xbox 360 character).
You should be able to play with your nephew on the Xbox 360 just fine. However, any items you gain on the Xbox 360 platform will only stay on the Xbox 360 character and won't transfer over to the Xbox One. I hope that helps you!
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Thank you so much! That is all I needed