Impacts of a surviving House of Bruce

So, this is something I've long been curious about. Given that Robert the Bruce and his son David II were both the figures that led the Scots during their wars of independence from England, had the House of Bruce continued to rule Scotland into the 15th and 16th centuries, how might this have influenced the development of Scotland? Would the feuding between different branches of the Stewart clan have been replaced by the feuding between Bruce and Stewart? Or would the fact that the Bruce line has continued nullify the threat the Stewarts posed to David II otl?

Furthermore, should a scenario emerge where the House of Bruce ends up ruling England as well, how might that affect dynamics between the two Kingdoms? Considering how the Bruces are seen as being linked to the struggle for freedom and all that.

A possible family tree for descent:

Robert I of Scotland (b. 1274: d. 1329) m Elizabeth de Burgh (b. 1284: d. 1326)

Had one surviving son and a few daughters.

David II of Scotland, son of Robert (b. 1324: d. 1371) m Joan of England (b.1321: d. 1369)

Had issue: Robert II of Scotland (b. 1346)

Or alternatively:

Robert I of Scotland (b. 1274: d. 1329 ) m Elizabeth de Burgh

Two surviving sons and daughters:

David II of Scotland (b. 1324: d. 1371)

John II/ Robert II of Scotland (b. 1324: d. 1384) m Isabella MacDuff, or Margaret of Mar.
 
Alternatively, another brother of Robert the Bruce surviving and leading the continuation of the dynasty would be great
 
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