Hugh & Esther's daughters, Margaret (my 2nd great grandmother) and Rebecca, were baptised at St Mary's Carlisle on the 12 Feb 1832. Hugh is on the 1841 census living at Wigton not with Esther but Mary. Margaret & Rebecca are also on the census as are 2 other children, Jane & Elizabeth. I don't think these other 2 girls are Hugh's daughters but probably Mary's from a previous marriage as they were born in Belfast Ireland.
Esther must have died between 1832-1841, as there is only one Esther Hamilton in the death indexes which I now know to be the wrong one, she must have died before registration began and would either be in Carlisle or Wigton. Hugh died in Apr 1842 just a month after the birth of his son William. I can find no trace of a marriage between Hugh & Mary.