I don't think so.......
I assume you will both continue to live in the Republic of Ireland.
There is a joint tax agreement between the UK and Ireland, for those who live in one country and work in the other.
I don't know the details, but the broad principle of it is that you pay PAYE in the country that you work in, but must also put in a tax return in the country that you live in. The tax that you have paid in the other country is taken into consideration.
If you paid 10K tax in the UK and your tax bill in Ireland is 12K, you only pay the 2K balance.
I don't know exactly how this would work with a married couple, each working in a different county, but I 'm pretty sure that the tax authorities in both countries will not allow you to use this situation to double up tax credits.