There cannot be a vote of no-confidence because the government used an OIC. A no-confidence vote comes after a government proposes legislation, but the majority of MPs vote against it. A no-confidence vote is called, and if the majority votes "no-confidence", the government is dissolved and an election is called.
You are correct on there cannot be a vote on the OIC but there can be a vote on other issues which the opposition could tie back to the OIC. This required participation and negotiation with other parties.
If the NDP and Bloc were against the OIC they could easily partner with the conservatives on a separate legislation item or bring forward their own motion and vote on non-confidence. Look at the Mark Norman review -- one Bloc member voted to block the review and it was dead.
The use of an OIC was a slimy move and now with the bought press -- Global / CBC the narrative is being spun the way the Liberals want.
I do agree that this is not East vs West but this initiative was driven out of the East and was Socks response to the shootings in Toronto where as an election promise he said there would be better gun control targeting the voters in the greater Ontario region. It is also standard Liberal fare to divide groups --- recreational target shooter bad / hunters you are fine ---- now start the fight internally within those groups with public perception against the scary target shooters.
