You have a double tax issue here.
The answer to your question is 1. for payroll taxes (Assume you are an employee). On employment income you (generally) pay taxes where work is carried out. Work in NI - pay UK payroll taxes, work in ROI - pay ROI payroll taxes.
However, as ROI resident you may well be liable to ROI tax on all income (including NI income) with foreign tax credit for UK tax paid.
This is a simple answer to a complex issue and you need to get tax advice.