Here's the facts: this kingdom is divided in 5 duchies. Once upon a time one of them was a small indipendent kingdom itself, but was conquered and now it's a Duchy, part of the bigger kingdom with his own army (every Duchy has his own army, that added to the Royal Army form the main combat force of the Kingdom)
One day, the Duke, a descendant of the old King (when the duchy was still a kingdom) decides to rebel: The King, to suppress the rebellion, calls to war all the Dukes except one, who is left behind to ensure the safety of the region in case another kingdom decides to take advantage of the situation and attacks.
Kingdom Army: Each Duke has 2000 men and 200 knights and the King's army is 5000 men strong plus 500 knights. In total we have three Dukes and the King: 11.000 soldiers and 1100 heavy armored knights. It's a good army overall, every soldier has a shield and a sword and has got some protection, like helmets and medium armor. The morale is not very high. The kingdom army doesn't have siege weapons. The cavalry will be useless. We will see why.
Rebels Army: We have 5000 soldiers and 200 knights, led by the rebellious Duke. But they are not alone: a lot of peasants are supporting the rebellion. 5000 peasants wants to fight. The peasants are not armed like the soldiers, they don't have much protection and their weapons consists in longbows, clubs, rusty knives and swords and other crude weapons. Some of them have leather armor, but in general they have really light protection. But, they are ferocious, motivated and eager to kill the invasor. The morale is very high.
Scenario: The rebel army occupies a small fortress on one side of this river. The fortress is old, almost a ruin. On the other side of the river, we find the camp of the kingdom forces. The parts will meet in the early morning in battle. The river is dry, in the sense that the water isn't there. But, it rained a lot the last couple of days, and now is basically a river of mud. The mud's height is about 3.5 to 4 feet. So, the knights are forced to fight dismounted, they can't charge the enemy with all this mud. The King doesn't want to wait for the siege weapons: the rebels have to be crushed fast. On the other hand, the rebels have to fight, because if the kingdom army builds siege weapons, they will be forced to fight anyways, or the fortress will be taken down with them inside.
So, both parts will meet in open field, with only this river of thick mud separating them, in wich most likely the main part of the combat is going to happen.
How the rebellious army, with low armored but angry and motivated troops could win this battle?
P.S. Sorry for the bad english