Mate in 3
You aren't wrong. There are several ways this can go down. That's why I mentioned this wasn't forced. However, if black doesnt' take the queen, he essentially has to move the queen, or else 2. Qh6 Rg7 3. Qh8 Rg8 4. Kd7 Kxd7 5. Bg7!
If he does move his queen, lets say to b8 to threaten the king or c8 to protect his pawn. then it could go
2. Qh6+ Ke8 3.Bxf6 The bishop can't take because it's pinned by the Rook. If he moves Kd8, white can move Bxe7 and he's protected by the bishop. The queen is on the run with a relatively threatening attack. Of course, that doesn't change the fact that this puzzle is not perfect, and for that, I apologize.
Any way I can slice it, though, ends up with white with a nice advantage.
Let me know what you think.