Hello Thomas
Firstly have you obtained certificates of birth; marriages etc to give a timeline. Also have you checked the census of 1901 and 1911 to see where they lived then. Links are available on this site on the St Peters Parish page.
I am not familiar with the name St Peters Parish 2, there is a catholic and Church of Ireland Parish in Drogheda in the diocese of Armagh (a long way from Drogheda).
Was the McAleer family protestant (just by the name). Drogheda would have been fairly industrialised about that time and to leave for Galway to work with Dublin and Belfast so close is unusual. Drogheda had had a big linen industry and at the time had engineering works etc. Also a very busy port with a service to Liverpool including regular passenger services.
Do you know what a moulder was.
I will speak to a few people here, there are many O'Briens but it is a very common name (the first ever surname in Ireland I understand).
I have posted a number of links on the specific parish home page including http://www.jbhall.freeservers.com/
In St Marys Parish Graveyard of which I have the record book (opened 1902) there are 2 McAleer graves (of more recent vintage) 4 Brien graves and 34 O'Briens. The inclusion of the "O" in a name was a moveable feast as often it was out but in more recent times it was included but you should check under both.
I do not have the records for St Peters Graveyard but they are available in the local history section of the library here for reference only. There is an older closed graveyard called Cord Road which is also recorded as are the main Church of Ireland graves. There were also smaller graveyards.
Drogheda is a very historic town (founded in the 12th Century). I have posted some info on the St Marys Parish page and will be posting it on St Peters Parish Page in the next.
I live locally so if you can specify what you would like to know I hopefully can be of assistance and also advise you on the town.
Regards
Pat