Cook the potatoes in boiling, salted water until tender, then drain. Meanwhile, put the rhubarb in a saucepan with 3 teaspoons sugar. Cover and cook over a gentle heat for about 10 minutes, shaking the pan from time to time, until the rhubarb has partially broken down.
Remove 1 tablespoon of the cooked rhubarb liquid from the pan and put into a small bowl or cup with the mustard. Mix, then beat in the olive oil. Add the spring onions, stir to mix and set aside.
Add the beetroot to the rhubarb, then add salt, black pepper and more sugar, if needed. Toss the drained potatoes with the spring onion and mustard dressing and keep them warm while you cook the black pudding.
Heat the vegetable oil in a nonstick frying pan, add the black pudding and cook over a medium heat for about 40 seconds on each side. Put the potatoes and black pudding onto plates and serve with the rhubarb relish, sprinkled with caraway seeds.