Depending on how much riding you are going to do and the kind of workout you want you don't even have to switch out the tires.
Switching to smooth tires will provide less drag and a smoother ride, but it's not necessary.
I ride my mountain bike on the road all the time.
As far as the kid seat, though. I would depend on how your bike is set up. Mine, for example (like the one below but older) probably could not accomodate a center-mounted one.
Bring your bike to a good, full service bike shop and let them guide you.