That's actually an excellent question, and in my own experience I have found some interesting challenges with that. I guess I would say to you that in a coalition the differing rules of engagement present both a challenge and an opportunity. They present a challenge because it's sometimes difficult to rationalize which country is prepared to do what kind of mission. But they also present an opportunity, because some countries will be better able, by capacity, inclination, and rules of engagement, to take on some missions, and some nations will be more attuned to others.
If you're a commander of coalition operations, or even NATO operations, where sometimes nations still come with their own national restrictions--sometimes caveats, sometimes things they're more inclined to do--under those circumstances you have to find the right balance. Truthfully, you have to find the same balance among individuals. Personality often comes into play as well. Not all commanding officers are the same. Some are more aggressive, some are less aggressive, and some are cautious. They present the panoply from left of arc to right of arc, in terms of capability, inclination, energy, etc. So a commander's job is to get to know the people working for him and try to match the people to the mission, be it by nation, the skill sets they may bring to their units, and all of those things. It can be a complex business. Generally you will find that they operate with a matrix that shows the various nations and their different rules of engagement, and they use that matrix to optimize how they assign targets to get the best job done for the mission.