The Stewarts operated on different conditions than the Bruce would've. No regency by the Duke of Albany, capture of James I, maybe surviving Lords of the Isles. Butterflies people, butterflies....
But there's no reason why a Bruce king is going to be immune to those kind of problems. This gets into individual rulers and not something where "dynasty" tells us much.
Two things that come to mind:
David II's son - call him Robert after his grandfather - is going to be in a very different position than OTL Robert II (no sons to worry about, and much younger) in some ways. He may need a regency depending on when he's born.
The Stewarts are going to be a thing that needs to be dealt with by the Bruces. They are the next closest to the throne.
Note that "dealt with" doesn't mean exterminated - just that they're a factor, and not necessarily a favorable one.