How do I move my family to new duty station while I go to AIT ?

Reclassing to 15E,
Currently an 11B in process of pcs'ing. I pcs
15 Nov 18 to ft. Carson. Already have hard orders to next duty station. I have 10 days of TDY en route to find a house And an additional 43 days of leave. I report to AIT 06 Jan 19. I report to my unit 06 Jun 19. Obviously will early report. The issue is I've called my new unit on how I can go about bringing my family with me and dropping them off in ft carson, getting a house and then going to AIT. They aready said they could not In- process me because I don't have the mos in my re class contract to be there. However is there any way I can in-process the base so that I can get bah and not have to pay out of pocket for a house while I'm off at school. As well as if I need to come in on leave and In- process if possible and continue my leave before I go to AIT. Thank you and anything helps.