I amended my return to be claimed as a dependent so now my mom has to mail her tax return in, these have different addresses so how will the IRS verify my mothers taxes?

The  different addresses should not be an issue.  Since your mom cannot e-file she just has to print, sign and mail her own return.  She does not have to wait for your return to be amended--since that will take about 4 months.  The IRS will process her return that claims you as a dependent.    You do not have to live with her to be a "qualifying child.'  (Are you a student?)