If someone misses a child support hearing and an FTA is issued (along with a $1000 purge), what motion needs to be filed to dismiss both?

Your boyfriend will need to file a motion to recall bench warrant and motion to dismiss the failure to appear.  Each motion will need to include specific language to meet the burden for the Court to grant both motions.  The motion to dismiss the failure to appear and to recall the bench warrant would be based upon him not having notice of the hearing and thus his failure to attend was not an intentional act.  Additionally, he has has been paying child support through his employer withholding child support from his paychecks, thus he did not have any knowledge that there was any issue with his child support payments.  One issue he may have is with his failure to update his address with the Clerk when he moves or with DOR.  He has an ongoing obligation to keep his address updated which would avoid such issues.  Also, in regards to the purge amount, the issue may be with his employer not withholding sufficient child support payemnts of is they are withholding the maximum allowed in Florida, which is less than his obligation.  If that is the case, then he needs to petition to have the child support modified.