It's been a long time since my kids were that age but...
Franklin Institute - I haven't been down to that area in over a year so take this as "dated" info. You'll live but be vigilant, like you would in any city with moderate to high crime. Depending on where your hotel is, same thing. I don't know about the trains, I never used them inside the city proper. I'd Uber or rent a car, personally. (totally understand the car seat issue, though) The museum has a parking garage, if you go that route.
How are you planning to get to Sesame Place from Center City? SP is in a suburban area, right between higher and lower wealth areas, with nothing extraordinary to be worried about re: safety. I think it's still early enough in the season that SP won't be the mad jungle it is in the summer. At peak times, the park itself can get overrun with typical trashy theme park types.
If you're going to have access to a car, or consider renting one, also check out
Dutch Wonderland in Lancaster. Depending on the age of your kids, it's great.