How to improve faction relations from a very negative value

I don't know about the the diplomacy mod, but the only way I know of to make peace between two members of the same faction is done by talking to your spouse and asking if there's anything to improve your standing in the kingdom. Every once in a while, they'll offer a mission where you can go make peace between two lords in your kingdom (hopefully one of them will be the king).

Another indirect way of improving relations is getting your king to grant that vassal a fief. You can lend your weight behind a lord by talking to them and choosing the option of supporting them in their claim to some fief. If the king does grant them the land I'd imagine that their relationships will improve. Keep in mind, however, that this will alienate the opposing faction. Politics in Caldera is very murky and unsatisfactory.

The damage potential of the lance is all dependent on the speed of the horse the faster you go and hit an enemy the more damage you do. Since the lances in a tournament are also practice lances their damage potential is rather low.

There are 2 ways to deal damage with the lance, you can either couch the lance (Keep running with your horse and suddenly you will see the lance level horizontally.) All you need to do then is hit the person.

The other way to deal damage is to click and hold and when close to an enemy thrust the lance and hit them. This together with the speed of your horse will increase your damage.

Now the first way isn't really possible since the arena is rather small, and couching the lance takes time.

So you are going to have to try and thrust the lance against enemies, at a high speed to do a good amount of damage. My tactic in this is I keep running circles with my horse keeping my lance in a thrust position, get some speed and then go straight for an enemy and hope you hit him.