Yes, kids can stay in pubs in Ireland when accompanied by their parent/guardian.
In general, kids can be in an Irish pub until 9pm. Specific pubs may have different rules regarding children.
You can bring your child (under 18) to a pub with you with some restrictions:
The licence holder (normally the pub owner) can also refuse to allow a child or children on the premises if they believe that doing so would be harmful to the child’s health, safety or welfare.
These are the official guidelines. You may find the rules are not strictly enforced everywhere in Ireland.
Don't come to Ireland before you've memorised Irish pub etiquette