I'm currently unable to brawl against Uthgerd the Unbroken in the Bannered Mare in Whiterun. I'm a Kahjiit, accept her brawl challenge, and after one or two hits Uthgerd draws her sword out and starts attacking. If I defeat her, she will be killed and unable to complete the brawl.

I would post your load order as I am almost certain that this is mod related.

Alcohol Recipes.esp
Cloaks.esp
Complete Crafting Overhaul.esp
EagleEyePerk_Half_stamina.esm
Furbag.esp
IMCN - Overrides.esp
Imp's More Complex Needs.esm
Jump85.esp
Populated Cities NPCListMaster.esm
Populated Cities.esp
Realistic Lighting Patcher.esp
Realistic Lighting.esp
RealisticWaterTextures.esp
retreat.esm
Sprint4.esp
WATER.esp
Weapons and Armor Fixes - Hacks.esp
Weapons and Armor Fixes.esp
AP Skyrim
Balanced_Alteration.esp
Balanced_Conjuration.esp
Balanced_Destruction.esp
Balanced_Illusion.esp
Balanced_Magic_Master.esp
Balanced_Restoration.esp
dD - Realistic Ragdoll Force.esp
DeadlyDragons.esp
dovahkiinrelax.esp
Nocturnal robes-wearable
SIDT.esp
Slightly Reduced Distance NPC Greetings.esp
Smithing Perks Overhaul - Balanced.esp
UFO - Ultimate Follower Overhaul.esp
WARZONES - Civil Unrest.esp
Immersive Patrols.esp
Chesko_Frostfall.esp