Is there a way for an adult with a valid passport to travel with a thirteen year old with an expired passport to Ireland?

Answer 1

It is not ok to travel on an expired passport. Why? because even though the country you want to enter accepts expired passports (which there is no such country), the airline will not allow you to board the aircraft. So, always make sure you have a valid passport and proper visa, if you need one, well before your departure date.
It does not matter if you are a new born or a 97 year old senior- you should have a valid passport to travel outside your country.