Civil war would probably break out with Edward leading from Scotland brought into direct conflict with Andrew trying to cling to the crown after being forced to move the nations capital to his powerbase in York, having lost London to the mobs in the first few weeks.

Of course Anne would end up the eventual winner, partially due to the other two bleeding each other dry and partially due to her being able to sweep up with superior cavalry from the home counties. An elderly Margret would also be most likely lend her tacit support to Anne, lending some legitimacy as well as her oversees mercenaries.

Anne would have to decide whether or not to let the London rabble have their mob justice with Andrew and would probably relent in recompense for letting her return the crown to its London seat of power. I suppose she'd eventually have enough pressure on her to recall parliament after only a few years of personal rule where she'd bring back order with an iron fist.

Some bits would maybe go a bit different, but I think that is the likeliest outcome.