There is no owner and no second-class account. Both of you are simply on it, equally. When one of you taps, the other sees it; when one of you hands a prize over, it comes off both lists.
If you and they both press something at the same moment, both actions are kept.
If they already had children on Okeedoo
Sharing goes both ways, so their children appear on your board too. If the two of you together would have more than 8 children, the link says so and nothing changes on either account until one of you makes room — the link still works afterwards.