Not parent, but : school in Edinburgh. We code-switched, although the term wouldn't be coined for decades yet. RP in school, some variety of Scots (or whatever we're calling it) outside school.
In school it's likely you were speaking Standard Scottish English. Received Pronunciation (RP) is an accent, not a dialect -- though most RP speakers speak Standard English, so there's a strong correlation between RP and Standard English. I've yet to come across and RP speaker who speaks another variety, excluding the occasional phrase or borrowed word.
Outside of school you were almost certainly speaking Scottish Standard English, rather than actual Scots. Scottish English is a branch of English that's been influenced by Scots and borrowed vocabulary from Scots, but isn't actually Scots. Almost no-one in the 20th century speaks actual Scots; those who do are immediately identifiable and generally hard for a non-Scots speaker to understand. The last vestiges of Scots language speakers are parts of Aberdeenshire and the Borders.
Sources: Highlander born and raised, living in Aberdeen for >10 years. One parent is a Gael whose second language is English, the other parent is from the Borders whose first language is that variety of Modern Scots. Native speaker of Scottish Standard English, with a little time spent studying linguistics and an interest in the subject.
