[edelweiss]

I don't know if you are the mother or father, but if you're the mom I thought I would mention that you can take the Women's Only cars during the morning rush. They mark where to wait for those cars on the platforms.

I've been on really full trains before 10AM (everyone shoulder to shoulder and back to back) and after 4PM until 7PM depending on the line. If you need to get somewhere during a higher traffic time perhaps you can ask people at your hotel for less busy alternative routes to get around. Some lines get more crowded than others.