For our 2nd trip, we did bring our 2-3/4 y.o. son. Because it was our 2nd trip, we didn't do nearly as much sight seeing (good thing w/ toddler). W/ tots, I would recommend some/all of the following:
good back carrier or short outings
a "kids day". We went to an aquarium and the Children's park. If it's good weather, could easily spend whole day at the children's park. (take subways everywhere)
Find a grocery store near where you'll be and get some familiar foods.
plan on maybe not being able to experience good Korean food...at least at places where you sit on the floor. We went to a great place we had found our first trip and DS wouldn't sit still. I barely got to eat because I had to keep holding him still.
Plan for baby sis/bro to get the older sibling a present
For us, DD "got" DS a Pororo watch (it's a children's character he fell in love w/ there) and another toy. It seemed to help him accept her.