Ok, I am going to throw my tuppence worth into this. I agree that Cornelius, was probably known as Neal, (the middle part of his name) was Peter a second name or a first name? I see one of the children has the same name. Based on my own family, I know that a brother would have married his brother's widow, for possibly a number of reasons, if the son that died was the eldest, he would have inherited the land & I know in my family they would not have wanted the widow to marry another and take the land to another family, the family would also have been concerned that the children would have been well taken care of. As there was no divorce the first husband would have died before the second marraige. I think you need to find the second marriage cert on it it would give the fact that Bridget was a widow and she may have needed dispensation to marry her brother-in-law. You also need to find the death of the first husband. I searched Roots Ireland for the second marriage, under the name Fallon & Small and the first names of Bridget & Rose but with no result. In looking for the death of the first husband, while not your man, I came across the following in the will calendars:
Deceased Surname Small
Deceased Forename John
Primary Beneficiary/Executor Ellen Small
Date of Death 12 Jun 1908
County of Death Cavan
You can look at this for free at http://www.willcalendars.nationalarchives.ie/search/cwa/details.jsp?id=… This man's death record stated that he was a victualler in Belturbet, so there may be more family in Belturbet that may hold the answers for you. His widow then died and I am guessing an unmarried daughter Ellie Small. You could contact the National Archives and ask for a copy of it. I have sometimes found more information that may reveal more about your family.
Deceased Surname Small
Deceased Forename Ellen
Primary Beneficiary/Executor Ellie Small
Date of Death 19 Feb 1916
County of Death Cavan.
I also looked up the civil records, they are available for free at https://civilrecords.irishgenealogy.ie
I found this one Name PETER SMALL Year of Death1864 Group Registration IDN/RSR District/Reg Area Cavan Deceased Age at Death 56 Returns Year 1864 Returns Quarter 4 Returns Volume No18 Returns Page No 61 all the images are not loaded up yet, but you can keep returning to the site and perhaps it will be available.
You could also put your story in the local paper The Anglo Celt, you can contact the editor at linda@ anglocelt.ie You could also contact Cavan Genealogy, at cavangenealogy@eircom.net they may have records that are not available online, the Library in Belturbet may be another place to contact, they may know local people that may be able to help you, as I live about 50 miles from Belturbet. What religion were your family, you could also contact the church as there may be headstones in their cemetery and the family may have donated artifacts to the church or be included in some of the memorials.
Do let us know how you got on. Regards Carmel