I don't buy this at all. We all work with people every day who are 'thrown together' as much as any football people. The team welcome and have to integrate new team mates all the time. If Coughlan and Brown have the right qualities and WANT to make it work, they will make it work. Ultimately, Brown's the boss now so, if Coughlan doesn't agree with his methods, he'll have to make a compromise or look for another role but there's certainly no reason to have doubts until there's a reason to have any. Why assume that two grown-up human beings won't be able to get on with each other?
Not at the decision-making level they don't.
Has your company ever been taken over or taken over another company? How much of the management survived?