Genuine answer. The SNP have said Betty can continue. Personally, I'd rather have a republic.
As for tracing an heir to the Scottish throne, the Union of Crowns came before the Act of Union and it was the Scottish King James VI (James I of Great Britain) who took over the English crown so we don't have to look too far!
Having said that, Betty is only queen because her uncle ran off with the American divorcee - if it wasn't for that, who knows who would be on the throne now.
It's never been explained why she is styled Elizabeth II as Great Britain never had a Elizabeth I - she was only queen of England. If you look at post boxes or Royal Mail vans up here, we don't have the EIIR cypher on any of them.