If she is carrying out her duties of employment in the UK, she is liable to UK tax and National Insurance on her UK shource income - she will not be entitled to a tax refund if she is claiming her full UK tax reliefs due.
As she is an Irish resident, she is liable to pay Irish tax on her worldwide income, but will then receive a credit for any UK tax paid up to the limit of her Irish tax liability.
This will mean in effect that she pays the highest rate of tax in either UK or Ireland, but not double tax.
Why do you think she is paying more tax in the UK? If she is a higher rate tax payer, the tax bands are much more generous in the UK, and the difference would not be that much surely? - of course this will depend on the level of her income.