Hi, I found a few things that may help.
Births of children to Edward & Anne:
Charles born 1845
Mary born 1848
Anne born 1853
Catherine born 1856
Alicia Anne bap 6 Feb 1859 Drumcree, Armagh
Francis bap 13 June 1864 Portadown, Armagh
* parents are Edward Hughes & Anne O'Hagan.I could not locate a marriage cert for the parents. I also could find no birth for a child Sarah to Edward & Anne.
As to John Hughes, you would need more info than just his name to figure out which records would be his. There are far too many John Hughes to just pick one out of a hat. Plenty of marriages for and children born to John, but without the minimum of a first name on the wife, its a needle in a haystack. Would you have any idea of the birth years for Sarah, Ellen & Francis who you say are John's children? As to Elizabeth & Isabella, they could be children of a 2nd marriage or children of a child of either John or Edward.
Do you have a death of either John or Edward? Even tho' death certs have next to no info on them it is possible you may get John's wife's 1st name on it if she was the informant. Without more info its hard to go further.
As to births of Edward Hughes & Anne O' Hagan, I checked 1805-1825 in county Armagh & found the following;
Birth Anne O' Hagan/ Hagan:
bap. 6 Jan 1821 Upper Creggan, Armagh Roman Catholic parents: John O' Hagan & Catherine Keegan
bap. 27 March 1814 Armagh, Armagh Roman Catholic parents: Edward O' Hagan & Sarah Hughes
Birth Edward Hughes:
address: Tobermesson
bap. 22 July 1818 Clonfeacle, Tyrone
Roman Catholic
parents: John Hughes & Brig McSherry
bap. 19 Dec 1819 Armagh, Armagh
Roman Catholic
parents: William Hughes & Ellen Hughes
bap. 26 Dec 1819 Armagh, Armagh
Roman Catholic
parents: Peter Hughes & Mary Donnelly
bap. 22 July 1820 Armagh, Armagh
Roman Catholic
parents: Peter Hughes & Catherine Quin
address: Ballicromy
bap. 20 May 1810 Armagh, Armagh
Roman Catholic
parents: Edward Hughes & Ellen Filloon
address: Rathtrillick
bap. 20 May 1823 Tynan, Armagh
Roman Catholic
parents: James Hughes & Alice Hughes
If you find anything else let me know and I will look again. Hope something helps, Kim