A lot of what the previous poster says is correct from my experience. That said, never say never.

A very good place to look for Venice hotels is Kayak. I've found good deals in Venice with this consolidator site (it includes venere). You can also go to trip advisor and then look up the individual sites of well regarded hotels -- and hunt for specials -- but this will be time consuming.

If you can't find accomodation for 3, you could consider staying in Mestre, the mainland railway station that's only a couple minutes by train to the Santa Lucia station. There are chain hotels there that are more likely to accomodate 3.

Good luck, and let us know what you find.