If the mother has no intention of selling, mortgaging or transferring the house, there is in my opinion no pressing need to take out probate at all. She can live out her days in it and when she dies, the house can go through probate then (when it needs to be sold or passed on to next generation). Or she can simply wait and see. Probate can be obtained in circa 3 months, so if she decides to sell, mortgage or transfer, she just needs to give her solicitor a bit of notice to get on with the paperwork.
That said, an estate which at this stage consists solely of a house should be a fairly simple probate. Excluding probate office fees, the legal costs are unlikely to exceed €3,000 and might conceivably be as little as €1400 ( for a VERY straightforward probate I have on occasion charged €1200 plus VAT - tbh, it is unlikely that you could get it done at this level, but not impossible)