Why don't you try an experiment? I assume you feel the hybrid is slow even when you aren't towing the kids? So, just swap the tires and put the 700x25s on the hybrid. 35s will probably run slower but it depends on tread and pressure. 35s just weigh more also and it's rotating weight.
You could be talking a lot of money to make wheel swap work since the entire drivetrain is probably waaaaay different. You may just want to invest in narrower faster rolling tires for the hybrid. I suspect the old roadie doesn have indexed shifting?
Why not just ride the roadie when you want to go fast and ride the hybrid when towing the kids.