Wi: Alexander III of Scotland had a brother

Alexander III was born in 1241 and died in 1286, of course before he died his sons Alexander and David had both predeceased him causing him to recognise his granddaughter Margaret Maid of Norway as his heir, he of course re marired to Yolande of Dreux in the hopes of siring an heir before hand. He died before this could happen in 1286, and Margaret's death in 1290 prompted the great cause of Scotland.

Now what I am wondering is, if Alexander III had a brother say born in 1243 who was still alive when his brother's children died, what would happen? Would Alexander remarry? If his own brother had children and they had children? Would Margaret even be named heir to the throne?
 
A deal would probably be made for Margaret to marry a grandson of Alexander's brother, but Alexander's brother would most likely take the throne. Alexander would still remarry, because almost every King prefers to have an heir of their own body over a collateral relation inheriting. Seems to be the conclusion I can come to.
 
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