The below info doesn't categorically answer your question, but may be a good starting point, I think in the end you will need to write a letter to the justice minister to formally change the immigration status of your mother when she is here (most likely to stamp 3 or stamp 0 subject to renewal- I'm not aware of any retirement visa - she may come here thou on short stay family visit - not sure if that's the way it works). What is vital to prove is that she will not be a burden to the state. It may help your case if all of your family here are already Irish, but as always everything is dependent to the Minister's discretion.
[b]Non-EEA nationals: citizens of certain non-EEA countries must apply for an entry visa before they travel to Ireland. When you have arrived in Ireland if you are not an EEA or Swiss national you must have permission to remain if you wish to stay for more than 3 months. If you are retiring to live in Ireland, you must be able to prove you have sufficient resources to support yourself and obtain permission to remain by registering with your local immigration registration officer following your arrival in Ireland.[/b]
http://www.citizensinformation.ie/en/mo ... eland.html
One good avenue thou, is get your Irish citizenship then move to UK (get a permanent job), then you can get your Non EU mom as a dependent (please research EU treaty rights). I'm not sure if the below links are the correct ones, but as I said, may be a good starting point for you to get you going.
http://www.ukba.homeoffice.gov.uk/eucit ... ts-family/
http://www.ukba.homeoffice.gov.uk/eucit ... /applying/
good luck.
