You may wish to begin by determining what her support system is in Ireland. Do you have extended family, friends and relatives there? What services are available to her? Have you asked your mother where she prefers to live? It is understandable that you wish to have her here with you, but it may help to explore options and establish a plan for a short term and then longer term solution, such as moving to the States.
If she has dual citizenship, there are limits on Medicare/Medicaid coverages. If you are her sponsor, her coverage is based on your income. You need to consult your state Medicare office for details. The process to file and process a Petition for Alien Relative can be rather lengthy and sometimes frustrating. I advise you to consult an immigration attorney, preferably one who specializes in family immigration law. You will need to provide proof of things such as relationship, your residency, legal status and the ability to provide financial support for your mother.