Why does it still shows my other child's school name in the "Your tax breaks" page, even though i entered his school name?

Try 2 things:

First, Go through the education section again. Go through the entire education interview until you reach a screen titled "Your Education Expenses Summary".  Click edit next to the student's name. That should take you to a screen “Here’s your Education Summary”. Click edit next to the school name. The next screen shouls allow you do edit.  Check all info, particularly the school's tax ID#

If that doesn't work, Go through the entire education interview until you reach a screen titled "Your Education Expenses Summary".  Click delete next to the student's name (you cannot change  it and you cannot save your entered info).  After you confirm your deletion, the next screen will allow you to add a student.