Sir William's talent seems to be limited to endlessly charging about on crusades. So it doesn't come as a surprize that he even needs help with gaining honour to become Royal Champion.
You lose control of your home estate Harbury and are now the "proud" owner of Sir William's estate. The economy of Sir William is a complete mess. You start out with low resources, but you have a lot of money, so you can easily buy in wood and stone as needed.
First off, erase the barracks and the armoury and the little bit of wall that protudes inside. Now place the Royal Kitchen in their place, build two or three apple orchards and 5 to 8 huntersposts. Three or four dairy farms can be placed outside the castle. Place four gong pits - near the stockpile, the kitchen, the granary and the dairy farms. Add three falconers posts - two inside one outside of the walls. Also place the Lady's Bedchamber near the keep and buy in 30 units of cloth. That'll keep the missus busy and brings valuable honour. Add two pig farms and three eel ponds outside the castle for feast meal production. If you followed the alternative route, you can also cart in some vegetables from Boorswell.
Don't forget to rebuild the Whittle estate, which is now owned by you. It is specialized in bread production, so if you don't want the AI to place the buildings all over the place, do so yourself.
Keep an eye on the happiness of the people in your estate. As long as they're kept happy, you should have the neccessary honour way before the time runs out.
If you followed the advice and gave the troops marching orders, they should be walking off towards Sir Grey's castle, even if you can't control them anymore.Start building up your new estate as described above. Once that is done, it is time to transform Whittle into an industrial powerhouse. You will notice that you can't erase the walls of the former outlaw camp with the eraser tool, so it is time to use the most powerful eraser tool of them all - the Lord's kitchen. Buy in about 100 units of stone and place the kitchen IN the wall. Now erase it again and a segment of the the wall is gone. Continue to do that until you have deleted most of the walls. Now you have plenty of building space.
Place the Lord's kitchen (without deleting it this time), 10 eel ponds, 5 wine yards and 10 vinters huts. Down in the village add bread production buildings (before the AI does) and as space permits a few dairy farms as well.
If space permits, you might want to add a few pig farms in boorswell as well. Now you have all set to make mission 12 a complete walk-over.