Maybe I missed it, but why couldn’t House Tully declare the Freys disloyal bannermen, take the bridge, and put them all to the sword? Or Robb just conquer them outright? It seems like it would have saved quite a bit of trouble.

In both cases, because you’d take significant casualties while doing it, and in the end only make your realm weaker. (Although Robb has the added time pressure of needing to get south, relieve Riverrun, and save his father)

Also, vassals don’t like it when their liege lord exterminates a fellow vassal – it gets back to the “better feared than loved as long as you avoid hatred” thing. Vassals tend to call that kind of liege lord a tyrant, and that tends to lead to rebellions, assassination attempts, Lords Declarant, etc. the moment you suffer a setback.