It's always a difficult balance between allowing the players freedom to do what they want (especially in-character), while keeping control of the story and being "ready" for whatever surprising behavior they produce.

The splitting up is always risky. But in the first instance, it sounds like you had created a sense of urgency that can cause that sort of thing. In the second case, it sounds like their approach might work for investigating without triggering combat, if handled right.

Behind the scenes, the tough part is whether to modify the amount of enemies in a given situation to deal with the unexpected splitting of the party. You can't compromise some encounters which are climactic (because making them "two-man"-able could rob them of their drama), but less plot-essential fights might be reduced a little (possibly putting the enemies somewhere else later on), because in the end, you don't want to discourage them from splitting up *ever*. A lot of the time in books or movies, one or two protagonists have to go off on their own.

And no, they NEVER run away. If I can convince the players to run away, I'd be very proud of myself.

Looking forward to hearing what happens next...