Starting with the 1911 census -
Dwyer household 1911The family are RC, all are Co. Wexford born and the parents are married about 11 years, so c1900.
The first step is to try to establish Bridget's maiden name. The best way to do this is to search for a birth of one of the children. The youngest child, or sometimes one with the least common name, is usually the best to search for. The town of Enniscorthy is located in a registration district of the same name, so that narrows down the area. (see the introduction link for the BMD Index)
There's just one good match for the birth of Edward jnr, so that might be the place to start :
Name: Edward Dwyer
Registration district: Enniscorthy
Event type: Birth
Quarter and year: Jan-Mar 1907
Volume : 4 / Page : 541
A cert for that birth will show details such as father's name and occupation, place and date of birth, mothers maiden name etc. Once you have a confirmed maiden surname the search for the marriage is much easier.
It might also be an idea to then search for a birth cert for Dennis to confirm that he is part of this family. This index record looks like it could be a possible match to your clues:
Name: Denis Dwyer
Registration district: Enniscorthy
Event type: Birth
Quarter and year: Jan-Mar 1922
Volume : 4 / Page : 403
Shane