Got it! Is there a similar separatist/independence movement in Ireland? Or any movement dedicated to separating Ulster/NI from the rest of the island? How successful are they?Originally the party was just campaigning for home rule. When that was acheived in 1949 the SNP was quickly reorganised toward Scottish independence. William Wolfe led the party through two independence referendums in 1968 and 1977. But both were defeated, with 1977 being a close affair until Trudeau brought in some of his empire-wide reforms to the confederal governance system and distribution of powers. When they returned to power in 2003 under Alex Salmond they organised another referendum in 2006. Similar to the OTL 2014 referendum this was close, but ultimately won by the No side due to economic arguments (loss of access to British markets tariff free) and the EU saying Scotland would join the back of the queue (in order to not piss off the British imperial government).
Unfortuntely the SNP haven't been able to shake Scottish independence, described ITTL as "their obsession". Unlike IOTL there hasn't been a material change to Scotland's circumstances so appetite for another referendum wasn't strong enough at the 2017 election. To counter any independence thoughts it has been suggested to send a member of the royal family north of the border as the next Lord Lieutenant.
The SNP have been following a logical process from regionalism -> full home rule -> independence. There is a regionalist faction of the party, that espouses a relationship similar to the associated states in the Pacific - recognised independence but tied to the United Empire for defence, foreign affairs and economic matters - but they are a small, but growing minority. The suggestion of most nationalists is Scotland becomes an independent Commonwealth realm at first, and then move to either a republic or a separate monarchy in residence.
Looking ahead, I imagine that if the SNP lose the 2021 election then the regionalists will probably displace the nationalists as the dominant faction within the SNP and independence will be relegated to the backburner and only rear its head every 40 years or so (or if something happens to undermine the Union).
Edit: to follow this, who are the party leaders in the Lords?