This assignment seems more in line with a Speaker of the Black Hand. Shaleez, the Argonian murderer of a Dark Elven family, has been located in Cyrodiil. Your orders say that this is a bit far for the Morag Tong, the assassin's guild of Morrowind, so the surviving family has hired the Dark Brotherhood to do the job.
Players of Morrowind would know that the Dark Brotherhood split off from the Morag Tong long ago and that the two groups have been bitter enemies ever since. Although they can only legally operate in Morrowind, the Morag Tong has performed assassinations all over Tamriel, so I don't buy the "too far" part of the orders. In Daggerfall and Oblivion, the Dark Brotherhood seems to be a splinter sect of the Thieves Guild. I'm not going to be the arbiter of what is and is not canon for the Elder Scrolls, so take whichever version you prefer. But for the most part, relations between the Morag Tong and the Dark Brotherhood have historically been "kill on sight," especially inside of Morrowind. Perhaps there is a rapprochement in the works.
At any rate, you'll find Shaleez in the Flooded Mine, which is north of Bravil. Except for when she sleeps, she spends her time wandering around the mine. You're told that she's a very skilled hunter, but she's actually 10 levels higher than you. She should have a couple of enchanted swords on her and, considering her level, you can bet that she knows how to use them. Be prepared.
Once she's history, travel to Fort Redman. The Fort is on the east bank of the Niben, just a little way north of of Fisherman's Rock (the "Mazoga the Orc" side-quest in Leyawiin). You'll find your payment and your next set of orders in a coffin that's just beside the door into the fort. If you're an aspiring Vampire hunter, you'll find a few of them inside the fort itself.