My ancestor Felix McQuade was born in 1847, County Armagh, (what is now N. Ireland).
He had siblings, of which only the names of two are known. Henry McQuade and Terence McQuade
Based on the info given in your post, it is possible that the Terence McQuade that is your ancestor, may be the brother of my ancestor Felix McQuade. Apparently from your info, both Terence and his spouse were born in Ireland.
The parents of these McQuades, if they are indeed brothers are:
Patrick McQuade, died 1891 Camlough, Co. Armagh
Rose McQuade (nee Rosa or Rose Trainor) died 1892 Camlough, Co. Armagh
Oh well, that's all the info I have. Possibly that may add pieces to your puzzle.