Many thanks for the additional information. I have searched the online bdm indexes for NSW with no success for Jesse.Elizabeth's age is derived from the Shipping Records as this family emigrated on the Morning Star in 1864 and also her date of death here in NSW.the family travelled out together on the ship and no Jesse is mentioned: Additionally Joseph's age is different to that of the 1851 census, while Mary Anne's,Francis and Joseph's are about right. Joseph senior appears to have lowered his age for emigration.
The list below is from the State Records online index: www.records.nsw.gov.au
SURNAME FIRST AGE EVENTS VESSEL YEAR REEL REMARKS ASHMEAD Anne 2Morning Star 1864 2139, 2482 and family ASHMEAD Elizabeth 10Morning Star 1864 2139, 2482 and family ASHMEAD Frances 18Spitfire 1863 2139, 2481 ASHMEAD Joseph 14Morning Star 1864 2139, 2482 and family ASHMEAD Joseph 46Morning Star 1864 2139, 2482 and family ASHMEAD Mary Anne 41Morning Star 1864 2139, 2482 and family.
Given the gap in the children as per the 1851 census, it is quite probable that you are correct about Mary Anne being a second wife.