You can put the information on-line yourself by using any of the companies such as Ancestry. (You would need to join and pay a fee for access to most of the sites). If you want to publish it as a book, there are simple do it yourself books available on the internet.
I don’t have access to any photos of your family. You would need to find any living descendants and ask them for that. Matilda Bor(e)land (snr) looks to have had another illegitimate child named Elizabeth born in Dervock on 16.8.1902 (no father’s name given).
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_retur…
So that Elizabeth may well have married and have living descendants but you would probably need to employ a professional researcher to investigate that. Matilda and Elizabeth in 1911:
http://www.census.nationalarchives.ie/pages/1911/Antrim/Dervock/Dervock_Town/129410/
Likely death for Matilda Boreland on 19.2.1937 aged 67 in the Ballymoney registration area. You can view that death certificate on the GRONI site (see below). The informant’s name might give you a clue as to what happened to Elizabeth. Matilda does not appear to have left a will.
I looked at the passenger list for Matilda Morrison’s journey to New York. (She arrived in New York on 27.4.1901 on the Laurentian. She was not travelling with anyone named Stockman. The other passengers were all young single women who were servants. Presumably all looking for work in the US. I would say Matilda was travelling alone. It’s some distance from Dervock to Magherafelt and I doubt Matilda knew James Stockman in Ireland. I’d guess they met in the US. (James went to the US in 1900. Matilda was about 13 then. They’d hardly have been acquainted in Ireland).
The Stockmans seem to have been a large family. James must have had about 9 siblings, so presumably he too has some family still in Ireland. But again finding them may take a bit of work. It’s not always very easy tracing forward to living descendants due to the lack of availability of recent records.
If you are applying for an Irish passport you will need certified copies of the relevant certificates showing that you are descended from a grandparent born in Ireland. You can order a copy of Matilda’s birth certificate from GRONI in Belfast for £15 (sterling) or from GRO Roscommon in Co Roscommon for €20 (euros). The GRONI option is slightly cheaper. Here’s how to contact GRONI. You can order certificates on-line from that site:
https://geni.nidirect.gov.uk
GRO Roscommon: https://www.welfare.ie/en/Pages/Apply-for-Certificates.aspx
Here’s some general advice about obtaining Irish citizenship. I am not an expert in Irish nationality law and procedures and if you have any legal questions you might want to consult a lawyer or immigration advisor who does have those skills.
As far as I am aware, you cannot claim Irish nationality through the birth of a great grandparent. Birth of a grandparent in Ireland does normally allow you to claim Irish citizenship but there are several steps to go through. Firstly, you will need certified copies of all the relevant birth and marriage certificates showing the link back to the person born in Ireland.
Secondly, if you are claiming through a father or mother who was not themselves born in Ireland, you need to apply to get their birth registered as an Irish Foreign birth. That takes about 6 months and costs €278 (euros). Once you obtain that document from Dublin, you can then apply for your Irish passport. (Not before). There’s reportedly a 3-month delay for new applicants and a face to face interview is also required. So you usually have to go to an Irish Embassy or Consulate for an interview. The passport itself costs €80.
Fuller information here:
http://www.citizensinformation.ie/en/moving_country/irish_citizenship/irish_citizenship_through_birth_or_descent.html