Cook potatoes in boiling salted water until tender; drain.
Peel and cube; place in large bowl.
Combine vinegar, sugar, mustard seed, celery seed and 1/2 tsp salt; pour over warm potatoes and toss to coat.
Cover and chill.
Just before serving, add corned beef, cabbage and radishes. In a small bowl, combine mayo, relish, onions, milk, mustard if desired and remaining salt; pour over salad and toss to coat.