On MTGO,empty graveyards, my opponent has chalice of the void on 1, i have an active bonus round and cast rite of flame. MTGO lets me choose (at least i think i can choose..?) the order to stack the triggers and i stack them so bonus round trigger goes on first and then chalice. Chalice resolves countering the rite of flame, bonus round resolves and put a copy of RoF on the stack, RoF resolves netting me 3 mana (as there is a RoF in the graveyard now).

So far so good, but how does this interaction work in paper? As i understand it, it's legal for me to "hope" that my opponent misses his chalice triggers. But if he does not miss it i want to ensure that my bonus round trigger goes on the stack before the chalice. Whats the correct and legal way to play this?