Please stop beating yourself up. It's a surprisingly common conviction unfortunately . It's slipped out there a few friends/husbands of friends etc have actually got convicted of this is the past. I'm not saying it makes it "ok" but on the scale of "badness".... Do you know what I'm getting at ?
Sometimes, nice people, who continually beat themselves up for their past mistakes , including what you've done decades ago, can make themselves soft targets for people's anger. So I'd work on being your own advocate and standing up for yourself. Your mistakes of 20+ years ago do not define you.
You'll get people on here come along, see your vulnerability for your crime of 20+ years ago and see it as a way to point the finger and come out with "it's people like you that killed my uncle " etc. yet someone with loads of heinous convictions and cares nothing for it , they'll try to understand and analyse. Don't make yourself a target any longer.
Nobody has the right to know your past information. And that includes a criminal record totalling one non malicious and stupid act.
Most countries won't have any issue. If you Google it - there should be forums etc with others who've been in your position.
I can hear your nice nature from your post. Have a good think about how you frame this to your daughter if you choose to tell her. Go down the "I made a reckless mistake that I know regret. Like all humans. Today I'm a stronger and better person .." etc etc. don't make yourself a target ready to be whipped and shamed. Own it and spin it on its head to "that's not me today ".
I hope you file this in the past where it belongs. Many many "criminals" walk amongst us, with stupid youthful crimes on their records that have long since been buried.