If Mother was a widow (so no spouse) - everything will pass in law to all of the offspring equally. Any of them can extract a Grant of Administration - i.e. no will, so no executor appointed. The best thing is for them all to sit down and decide what they want to do and then either act collectively i.e. decide that one will extract the Grant or, if there are issues, any of them can individually, and can unilaterally seek to extract a Grant.
Whoever extracts the grants then deals with the liabilities - so no distribution of any of the assets should be made until all of the liabilities are discharged.
Any of them can do this personally in the Probate Office or, if they prefer, they can appoint a solicitor to act.
If you/they google Grant of Administration Ireland, they will find lots of information on the Probate Office website page.
mf