Hi Lindarose, a number of things, I found his Patrick's baptism in 1855 and attach, it was in the diocese of Meath, that is south Drogheda, Dublin side of the Boyne (I live in St Mary's parish), mother is Mary Lynch, one of the sponsors has an unusual name, Wiseman I think.
It is odd the marriage is 4 years after the birth but the baptism entry you sent is sort of final proof, oddly there is no civil record to match, there was a hefty fine for not registering so that is odd too. Given the time lapse there could also be other births. Drogheda was a highly industrialised area then so I imagine any stigma or so called gossip might not be as great in a busy town etc I know in a rural area my GG Grandfather in a much more rural area in 1857 got married a week after the 1st child was baptised, however I cannot find the census here as you meniton, if you could find the 1911 census for the family there is a question on it for the number of years married so that if correct number given it would reinforce the marriage year.
If Patrick was married to Mary Lynch circa 1855 or previous in St Mary's there is no record of the marriage as records for St Mary's marriages are missing unitl 1874 I think, civil registration commenced in 1864.
The children of the later marriage you have dates for do not all appear to turn up on the civil record, I also looked at adjoining areas for some of them.
To sum up I think the 1879 marriage is correct, you could also look it up on the registers NLI site to see if there is more information but I doubt it. Why they were tardy on civil registration I do not understand as I mentioned the fine was severe. Also very puzzled by the census or lack of, the 1911 version is the question on years married.
There are a few private Facebook pages you might like, Drogheda Down Memory Lane, mainly old and not so old photos, also Drogheda Down Memory Lane - Lost Family, not very active but people look, there is another one I saw recently Drogheda Roots or such like, not a member yet, finally there is Louth Genealogy, there is a good site on Louth in general and includes list of thise deceased with a reference so if you see one that interests you I have some books on the inscriptions, the St Peters Cemetery one is actually online but requires some sort of membership, the 1916 deceased may be mentioned there or in Calvery which I have. See http://jbhall.clahs.ie/
Feel free to come back if any thing strikes you, also see a recent picture of the outside of the old morgue on the Drogheda DML FB page recently if that sort of thing interests you.
Regards
Pat