Didn't you tell Vlad to stay away from Mallorie? Who does he think he is? Well, he's about to find out who you are, and learn it well.
It is usually a good idea to drive to the Cab Depot in a fast car when you go to receive this mission (my favorite is the Banshee, but then again, my favorite car for anything is the Banshee), as you will likely need it. Either a very fast car or one with very good handling is recommended for this mission, and for that matter all missions that involve a car chase.
Once the cutscene is over, either get into your fast car or the Roman's Taxi which now appears in the garage (and which will serve nicely if you don't have something else). Drive to the Comrades Bar to confront Vla- Hey! Get back here, you little swine!
Yep, he's doing a runner. Take out his goons- if you picked up a shotgun in Jamaican Heat this is an ideal environment for it- then follow him out the back. Try not to have the shotgun armed while running, as you'll go slower.
Not that it matters much; Vlad had a getaway car stowed around back, and now he takes off. Get into your own car and chase him down- note that it must be the car you arrived at the mission point with, or Roman will be left behind and the mission will fail.
Follow Vlad as he winds through the streets of Hove Beach, making sure to stay decently close so as not to fail the mission, and he'll head down to the Navy Yard. Follow him, being careful in navigating the always-crowded and winding street down here, and soon enough he'll smash his car into a road work and try to escape on foot. Get out of your own car and follow him.
After the cutscene, you're prompted to perform an Execution- a special sort of kill that can only be done on major characters in certain situations. Vlad is only the first one of these. Executions are performed solely with the pistol- take it out, and note that the targeting reticule is flashing a red ring. This is the sign that such a kill can be performed (though it may well be obvious in other ways). Fire once, and you get a little cinematic clip of the end of Uncle Vlad. BOOM, HEADSHOT!
Enjoy your lengthy cinematic what follows, then enjoy the fabulous cash prize you receive- lifted from Vlad's pockets? Take a moment, too, to soak in that feeling of satisfaction- you've just catapulted the story forward, and there's no stopping now.