There are a few things for your husband to consider.
1. To be resident in Ireland under EU FoM he needs to remain within Ireland for at least 6 months per year. 'Continuous residency' requires absences of less than 6 months:
https://www.citizensinformation.ie/en/m ... -national/ Working full time in UK, even with weekend return is likely to compromise that. So its not clear he is actually an Irish resident once working in UK full-time, not matter what lease or utility bills he shows.
2. From previous examples, my understanding is that he is meant to be paying tax in UK and submitting tax returns showing tax paid back to the RoI. The UK is likely to take a very dim view of not paying UK tax. But obviously, check with professional sources in UK and Ireland as specifics matter here.
https://www.litrg.org.uk/international/ ... %20Ireland. The EU rule about maximum 6 months out is also likely to be relevant here, as he couldn't claim EU residency as defined by EU rules. I would recommend getting advice in writing from a professional who represents you, and not your employer, on this matter.
3. You can apply as soon as you qualify.
4. If your child wasn't born in Ireland they will need one naturalised parent before they can apply.
5. Day of departure and arrival into Ireland count as present as far as Irish naturalisation is concerned. (Note that UK makes its tax calculations for residency differently: any hours spent in UK count as a days residency for tax obligations.) Your husband can gather his qualifying residency over a 9 year period, but the final year needs to be 'continuous' (that is, only 70 days out.) Some applicants have been approved with work travel taking them over the 70 days (for example, they've had 100 days of work travel), but critically: very similar applications have also been refused. I've be very, very surprised if they accepted full time work in UK as acceptable absence in the final year. The fact that it is an Irish company is irrelevant, especially as it is likely he should be paying his tax in the UK. He can always submit and see what they say - it's only the loss of 175 plus some time, as he is free to apply again once he is actually present in Ireland again.