I have two children whose passports have expired ...

You cannot travel with expired passports. Go to your local county office store and find out what the procedure is for expediting a renewal of your kids' passports.

rercommend you contact the canadian travel agency in your local area. you can also speak to any travel agent for the answer.

Here's the answer according to the State Department:

http://travel.state.gov/travel/cis_pa_tw/cis/cis_1082.html

ENTRY/EXIT REQUIREMENTS:  Entry into Canada is solely determined by Canadian Border Services Agency (CBSA) officials in accordance with Canadian law . Canadian law requires that all persons entering Canada carry both proof of citizenship and proof of identity. A valid U.S. passport, passport card or NEXUS card (see below) satisfies these requirements for U.S. citizens. If U.S. citizen travelers to Canada do not have a passport, passport card or approved alternate document such as a NEXUS card, they must show a government-issued photo ID (e.g. Driver’s License) and proof of U.S. citizenship such as a U.S. birth certificate, naturalization certificate, or expired U.S. passport. Children under sixteen need only present proof of U.S. citizenship.

So basically children only need proof US citizenship, and expired passports count as valid id's.

Cheers.