My parents are Irish and moved here when they were in their 20's. I was born here but solely have an Irish passport. It's a relatively straightforward process with the correct paperwork
If you're Irish, your kids can get a passport even if they're born in the UK and never even set foot in Ireland. Contact the Irish embassy in w12 and ask for forms.
Where are you from?
Where were your kids born?
Both my kids have three passports now (Irish [from me], UK [born here], and Canadian [partner])