Rinse the brisket with cold water and place in large, heavy pot or Dutch oven.
Cover with cold water and heat to boiling, skimming the surface if needed.
Reduce the heat and simmer, covered, for 2 1/2 hrs.
Add the carrots, turnips and potatoes to the pot and continue to simmer, covered, until the vegetables and meat are tender, about 40 min longer.
Meanwhile, place the beets in a saucepan and cover with cold water.
Heat to boiling, reduce the heat and simmer, uncovered, until tender, about 30 min.
Rinse quickly under cold running water.
Peel and transfer to a heatproof bowl. Keep warm in a low oven.
After the beets have cooked for 15 min, place the cabbage in a saucepan.
Remove 1/2 c cooking liquid from the corned beef and add to the cabbage.
Heat to boiling, reduce heat and cook, partially covered, until the cabbage is tender and all the liquid has evaporated, about 15 min. (Remove cover if mixture is too wet.)
Reduce the heat to low and keep warm.
When tender, transfer the corned beef to a heatproof platter and carrots, turnips and potatoes to a heatproof bowl. Cover and keep warm in a low oven. Save the cooking liquid.
Melt the butter in a saucepan over low heat.
Stir in the flour and both mustards.
Cook, stirring constantly, for 3 min.
Whisk in 1 1/2 cups of the cooking liquid and the vinegar.
Heat to boiling and boil until slightly thickened, about 4 min.
Remove from the heat and whisk in the sour cream.
Add salt and pepper to taste.
To serve, slice the meat and arrange on platter, Surround with the carrots, turnips and potatoes.
Serve the cabbage and beets in separate bowls.