I have Christopher C TIBBITS in 1850 census at Coldwater, Branch Co, MI with Julia (presumed wife). Julia age 24, C C age 24 is a blacksmith. Christopher married Julia HUNTLEY 04jul1848 in Branch Co. If what you say is correct, Julia must have died and C C remarried. Given the 1880 census entry it looks like Elizabeth remarried between 1861 and 1868. Perhaps Joseph Allen and James Byron were children of Julia born between 1850 and 1861.
If you have a census record for C C in 1860, would appreciate details.