As a UK employee your employer is obliged to operate UK PAYE and NIC.
As an Irish resident working 2 days a week in Ireland, the UK company is obliged to operate Irish PAYE on the relevant proportion of your salary.
This is a complex situation, and it is your employer's obligation to sort out.
They can not consider you a standard UK employee and assume you are working at a UK address - it is up to you to tell them that you are working in Ireland from home on the relevant days.
However, separate from the UK employer obligations, as you are Irish tax resident and UK tax resident, under the double tax treaty you are likely to be considered Irish resident, and not UK resident, and you have an obligation to file tax returns and pay correct taxes in each country - again this is complex.
I would suggest that you get professional advice
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