score:7
One would have to caveat the answer: Laws regarding child safety in Cabs may vary from state to state but here goes:
New York city officially exempts Cabs from requirement of Child Safety seats in Massachusetts you will need to restrain the child.
In Buses and commuter trains it is simply not possible to use a child safety seat at all as there is no equipment to secure it to the seat(in most buses). Furthermore unless you want to pay for a separate seat your kids are allowed to ride in your lap.
Strollers: on trains and buses you will have to fold them and stow them away from the aisle. On Subway the situation is somewhat different. Most parents I've seen leave the kids in strollers because there is no place to sit. Most passengers are understanding to the situation.
One thing I would suggest is getting if you already don't have one is a baby carrier for your 9mo.