Hi Shaz,
I am going to provide you with information to the best of my knowledge but I have been wrong before as I did not know about the agreement between Britain and Ireland hich states that there is no need for permits to reside on each other's shores.
There is a proper contact form on the Ministry of Foreign Trade's website. You must "click" on contact, then choose the FBR photo from the options offered. They have answered my queries in two days or fewer. However, if you need to speak with someone directly you may call the offices on Tuesdays and Thursdays between 10am and 1pm Dublin (Greenwich) time and they will assist you. The man I spoke with, Mel, was so pleasant.
You cannot translate your mother's document;, it must be translated by an unbiased third party, a certified translator by profession as this is a legal transaction.
I had my passport notarized in Turkey and assumed I needed to have the transaction translated since it needs to be clear and documented in English. The notary office provided me with names of certified translators and I hired a professor/translator to translate the document.
I am an English-Spanish translator as I lived abroad in a Spanish speaking country as a child(my father was a banker now retired); I would not translate my own document in a legal process, because I am a biased party and obviously it will not be valid.
Your "certified" birth certificate is a copy of the original in the file of the county offices of your birth city. It is rare for those to have their originals. My grandmother does but she saves EVERYTHING.
Proof of address may include: medical bills, bank statements, and utility bills.
All the best.