The Princes' Kingdom is a role playing game aimed at kids, that encourages thinking about values and constructive problem solving. Despite the name, the game can be played by girls and boys. While the rules suggest that girls and boys are both called "Prince", I recommend going with what your girls want, which is probably "Princess".
The game was written by Clinton R. Nixon, of CRN Games. Sales of the game support the American Friends Service Committee.
The basic concept of the game is that player characters are children of the King, and part of their coming of age is traveling from island to island in the kingdom. As they travel they are to help solve problems and ensure people know the King cares about them.
Each island can be radically different, so one could be an industrial center, another could be a forest city, etc. You and your players are in control of how much fantasy gets into the game, so there might be magic or not, science fiction or not, etc.
A Focus On Values
One of the great things about role playing with kids is it gives you the opportunity to put them into difficult situations, and let them think about the values associated with solving the problem. The Princes' Kingdom is designed for this from the ground up.
The King is a good king, and gives his subjects a lot of freedom. The King's children focus on doing good throughout the islands. So from the start you avoid some of the moral ambiguity that can creep into typical fantasy games that focus more on dungeon crawling.
The situations you create on the islands for your players can focus on specific values you want them to think about. If you have a child who has trouble sharing, set up an island where the citizens' lack of sharing is causing a variety of problems. Allow your child to see, in simulated form, the lack of sharing taken to an extreme.
The same approach works for any value your child is mature enough to think about.
The conflict resolution system uses a pool of dice for each character in the conflict, and involves bidding dice to accomplish actions or to block someone else's actions. The basic idea is that both players roll all their dice, and then whoever is starting bids a couple of dice. The other player must see that bid by pushing in however many of their dice it takes to match the bid. The more dice they have to use, the less successful they are at blocking the action.
There's some fairly sophisticated reasoning that has to happen here, when there are multiple ways to see a bid. It might be better to fail at one attempt in order to succeed at the next, for example. The sheer number of dice can also be problematical for kids.
One great thing about the system for kids is that players describe what happens when they are defeated. It isn't you as the GM telling them how their character was defeated, it's them. This encourages kids to accept defeat as just another part of the ongoing story.
Characters in the game average at 9 years old. Players that age will be able to handle the conflict resolution system. The youngest a character could be is 5 years old, but most players that young would not do well with the system.
Running The Game
The game is intended to be run from a basic island concept, without a lot of preplanning. You'll create some conflicts for the PCs to resolve, you'll create some of the basic citizens, and then adapt to what the players want to do.
One of the nice bits in the game is that it gives rules for creating a proto-citizen, a series of stats that can be given flesh when the PCs interact with someone who turns out to be important to the story. Instead of creating every NPC in the game in advance, you only worry about giving stats to the ones who turn out to be important.
This is more important than it sounds. In many games, the GM knows which NPC has vital information the PCs need. The PCs might flail around for a while if they don't interview that one NPC. Kids will get bored quickly with this.
The Princes' Kingdom approach is that whoever your players choose to make an important part of the story is an important part of the story. The kids feel like they're always moving forward and discovering something important.
To aid in this, you might also create some NPC roles. For example, you know that on a given island there will be a character who is an informer, who will tell the King's children what is going on. You don't have to figure out ahead of time who that is. Allow that to develop during player, based on what the players do.
I really like the game! The system is more complex than I'd like for kids, but it gives the kids who are in the right age range something to grow into. And the tie in with values and ideals is exactly perfect for role playing with kids.
You can get more info about buying the game at the CRN Games page for The Princes' Kingdom.