I could see the Dunmer refugees being forced to uphold ridiculous laws. If they ever break one of these "laws", their punishment just so happens to be quite severe compared to a Nord charged with even worse offenses.
Perhaps this could lead to quests involving proving some of these Dunmer are innocent, or to help them escape. Maybe we could try and catch the ruler of the city commiting some of these crime himself and blackmailing him to remove these laws. On the other hand, it would be cool to also have the option of siding with the Nords, and giving false testimonies stated the particular Dunmer were guilty, or helping Nords that were obviously guilty frame innocent Dunmer, or if you try to blackmail the cities ruler, accept his bribe to shut your mouth and be on your way.
To add the that, the local nobles, exploiting these racist laws, could extort Dunmer into paying them, or else perhaps the noble's men might just "witness" them committing some of these crimes. Some nobles might choose to press gang these Dunmer into service, essentially becoming slaves.
Some nobles will instead shift the blame from their terrible policies onto local Dunmer refugees. Crime is their fault, the banks having no money is their fault, the
civil war is their fault. Parts of Skyrim could basically devolve into early Nazi Germany, with Dunmer being blamed heavily and sent out of the country in bulk, or just outright killed, whether by law enforcement or by roving mobs who leave their brains at the door.
This could present the player would some interesting choices. Do you save a single Dunmer by fighting and killing several dozen citizens? They were driven to the edge by fear and lies, is it really all their fault that their lords are lying to them? With high enough speechcraft, players could convince them that they are being lied to, while warriors might fight their way out. Craft mages could simply make the Dunmer and themselves invisible and lead the Dunmer off to safety. However one attempts this, the greater problem will still be at hand (that nobles are lying and extorting) and the player may run into this scenario, or ones similar to it, until they fix the greater issue.