Welcome to Toronto.
Staying downtown you will not need a car. The idea of buying TTC, Toronto transit Commision, day passes is excellent. If you plan to explore some of the city's neighbourhoods, The Beaches (pease don't flame me because I didn't call it the
"The Beach"), The Danforth, The Kingsway, Queen West (your kids can get a piercing or a tattoo).
http://www.toronto.ca/ttc/family_pass.htm
But you probably won't need the TTC if you are planning to walk around downtown. The south end of the Eaton Centre is only 3 blocks north on Yonge @ Queen. Getting to the rogers Centre is really easy. If the weather is inclement just walk down to Union station and talk the Sywalk over to the Stadium
As for taking the TTC from the airport. If I was back packing it with a couple of buddies that would be great (save on beer money). But with two little ones and luggage, and all of the stairs and broken escalators on the TTC, a taxi or limo would be the way to go.
As for car seats, I never understood how they are required in your car but not on a bus or taxi? If my kids were still using car seats I would bring them. But that's just my preference
Enjoy Toronto