Not sure if this will help you any working back but there is an on line tree (on Ancestry) for a possible sister to Patrick called Mary born c. 1844 in Ireland to the same parents, death in Leith in June 1901. Also based in Midlothian with her family so you should be able to verify these details for yourself.
This is the 1871 census entry that is given for her and family - the children all show as born in Leith:
Francis Mcgovern 27, coal porter b. Ireland
Mary Mcgovern 27 b. Ireland
Mary Mcgovern 8
James Mcgovern 5
Eliza Mcgovern 3 Months
Address: 4 St Andrews Wynd, Leith
There are some IGI entries that seem to support this. There also looks to be some confusion as to whether husband's name was James or Francis (maybe he went by both) as there IGI births for their children under both James or Francis for father. The marriage, with groom as James, I think shows in Leith on 23 June 1862, with a James MCGOVAN marrying a Mary Cain. Lots of spelling variations showing for the McGovern surname, so you will need to use the exact spelling showing on IGI to find them on SP (McGovan/McGovarn/McGoveran for example, or search as McG*v*n on SP).
Possibility that for 1891 census in Leith, mother Mary Cain is now living with daughter:
Mary McGovern 49, Mill Worker (Flax) b. Ireland
James McGovern 26, Dock Labourer b. Leith
Mary Cain 83, mother b. Ireland
Thomas Buchan 32 boarder
Address: 59 Bonnington Road, Leith
Can't easily see the death of Mary Cain on SP which is showng as being in 1893 in Leith (parents John McCrann and Cecilia Padon). The only details for husband/father Edward are potential parents Owen Keon and Bridget Martin - no source info on this though.
Something to work on....!
Monica