Tyrande essentially is the law in night elven government, and Malfurion certainly isn't her "superior." He had been asleep for a majority of those 10,000 years, while Tyrande had to lead her people alone. He wakes up and starts trying to order her about. I'd be pretty miffed too.

As for her killing the Watchers...
What happens when one not only disobey the leader of a government, but gets in their way, especially during a time of war? They'd be swiftly apprehended. And what happens when they meet said leader with force? They'd most likely be met with force in turn.

She was trying to free Illidan, the greatest Demon Hunter. The big enemy at that point was the Scourge and the Burning Legion - undead and demons, respectively. A big risk, perhaps, considering his previous actions. But after 10,000 years of imprisonment, maybe she thought he deserved a second chance (whether he made good on that is questionable, but I digress...). Add in that he was Tyrande's childhood friend, and maybe you can see where she thought he might would help.

I think Maiev had a chip on her shoulder, not only from Tyrande being favored over her as High Priestess, but also because of Malfurion's affection for her.

But does any of this really matter? Who leads the night elven people now? And who went off to Outland after Illidan in a warped sense of justice?