OP I just did a tax search because the figures sound off. On your DP's income alone, with the child benefit for two children (not means tested in Ireland) his annual net take-home on that salary will be 78,115 euro - that's 6,500 a month not 5,500. Now that includes the children's allowance of 280 euro but your initial figures are definitely wrong.
If you were married, with you still not earning, that monthly take-home goes up to just under 7k/month, or 84k/year.
I know that people in high earning fields in Dublin can live in a bit of a bubble, and it is fairly unusual to only have one salary (much more so than in the UK) but that is still a very high joint household income, never mind a single one. Your 3 hours a day childcare will be totally free under the ECCE scheme your childcare for your under 6s will also be free. Based on the fact you're paying a peppercorn rent, you will have a LOT of extra money to play with.
I think it is worth a) calming down and looking at the long picture - you've taken one month's by the sound of it emergency taxed salary and been upset it didn't instantly solve your problems b) considering the financial protection and help of marriage and c) trying to do a longer term budget. Moneysaving expert is good for this. See what your day to day money is going on and if its worth it to you.
If you are looking at childcare beyond ECCE, there are now much more significant government contributions that can pay towards after school even with a high salary you'll get 1.40/hour off your childcare.