No, you should not include the dividend income on your tax returns if it was actually paid to your son even though he is your dependent. The IRS and state(s) should receive copies of the Forms 1099-DIV or 1099-INT your son received so if you don't include them on his tax returns, they may get confused and think he did not report all his income.
However, you may not need to actually amend his tax returns yet. Please review the following TurboTax FAQ to determine the status of your son's tax returns and how to proceed:
https://ttlc.intuit.com/replies/5170475