I had the exact same problem on the Pacific map last summer. I had to get a game operator to intervene before the two friendly stacks mauled each other. As it was, we both lost a unit in our multi-unit stacks.
Note that when you capture an enemy province, any other 3rd-party units that are en route to the provincial center are supposed to automatically stop where they are when the province changes hands. Another problem may arise when two un-allied forces are both attacking the same provincial center; when the enemy defending formation is destroyed, one of the attacking forces will be awarded possession of the province, but the other will immediately attack it. This problem is automatically avoided when both attacking forces are allies.