Wrongfully Claimed Dependants

A family member claimed my children as their dependants.  This person used to claim them when I lived with them.  I no longer live there and haven't since July 2018.  I am trying to file my taxes and want to claim my own children.  I'm not sure if I should continue to efile and claim them and wait for rejection then start a paper file, or if there is a more direct route.  The IRS has contacted this person asking for more info and forms to be submitted.  Please help me!  I am a single mom and desperately need this to be resolved ASAP.