This thread covers the weaknesses of HW's handling of presidential succession.
http://forum.juhlin.com/showthread.p...ght=succession
If you still want a scism you could have a missing member of the line of succession be found after someone further down the line was promoted to president. Milgov following the promoted SecDEF and Civgov following SecState who was missing and presumed dead for a while.
There could even be some intrigue about Military forces knowing the possibility SecState could have been alive but did not provide that intelligence and pushed the promotion of SecDef anyway.