Different children naturally handle conflict differently, even those with the same parents. I don't think you can draw any conclusions about discipline by watching a child's reaction. Also, for better or worse, a lot of (maybe even most) parents go easier on their children when company is over.
The general principle of expecting children to solve their own problems is a good one, but it's not something children can handle alone overnight. They need to be taught how the principles of fairness, sharing, and atoning for your mistakes apply in different situations, and they need the guidance of an adult for that, for quite a while.
Without adult guidance, the advantage skews to the child who is more aggressive or the child who is more adept at manipulating the rules to their favor. For example, my son will say things like, "Mom and Dad want us to share, so you need to let me play with your new birthday present right now." If the other child acquiesces, technically they have solved their own problem, but not in a fair way. It sounds like some of that is going on with cousins using the rules you gave your daughter to avoid sharing.
So rather than just telling them to fix it themselves, try to give them the guiding principle to apply in that situation:
- "You broke my tower after I asked you not to. What do you think you should do to make it better?"
- "How do you think you would feel if you had a brand new birthday toy? What's another way you could have something to play with, without taking a new toy from someone else?"
However, the principles you give should focus on things the child you're instructing can change, which is her own behavior. Yes, you're intervening, but intervening to force one child to do what another child wants should be rare, such as when correcting an injustice like one child hitting another to take his toy.
It's a tricky balance to strike. You want your child to be comfortable coming to you with problems, and know you have her back, but you also want her to have the tools to deal with those situations when you're not around. Fortunately, you have plenty of time to prepare her for that.
As far as how much intervention is appropriate with your niece versus your own child, I agree with @balancedmama that it's really a separate question, but in a nutshell, I think if the child is specifically coming to you, you should treat it the same as a request from your own child, unless her parents have asked you differently.