Ultimate Grilled Cheese : Keeping it together
Ignore the purists. If it's got cheese in it, and you're grilling it, it's grilled cheese.

The problem is this: your cold ingredients are keeping the cheese from properly melting through. The cheese is what binds the whole thing together. If there is not enough cheese, or if the cheese hasn't transitioned completely to gooey deliciousness, the sandwich is going to fall apart.

The solution is to heat your cold ingredients (at least to near room temp), and to cook the grilled cheese longer, at a lower temperature, so the heat has time to penetrate before the bread gets overcooked.