I think I must have misunderstood you. I thought when you were talking about fear of civil war, you meant that it was unlikely because people feared how awful it would be. Should I have read it as civil war could have happened because there i evidence that people fared that it could happen?
I think people were very scared of a return to civil war, which would (much like OTL) encourage them to seek the least complicated options - in this case, namely accept Margaret as their legitimate monarch and then coerce her to wed an agreeable King/Lord Protector of their (whatever your faction) choosing. It could have happened, without a doubt, but I think in this scenario it would encourage unity to avoid it happening.