If I am owed back support, and they have taken the other parent's tax refund, how long will it take for me to get it?

Call IRS.

It does not happen overnight. Usually takes about six months until you actually receive the intercepted tax funds.

Stop the IRS from garnishing your tax refund using tax form 8379 to see detailed instructions go here http://www.infobarrel.com/File_Form_8379_to_Recover_Tax_Refund_Losses