I found a company that makes this potato salad commercially and they had the ingredients posted. It sounds alot like catalina dressing(made by Kraft). Posted below is a recipe for a dressing similar to catalina that matches the ingredients posted. Besides red skinned potatos, walnuts and green onions they also included bacon bits.

Sweet Tomato-y French

2/3 C ketchup
1/2-1 C sugar (to taste)
2/3 C vegetable oil
1/2 C red wine vinegar
3T lemon juice
salt to taste
1-2 cloves garlic (or 1-2 tsp.)
2 T finely minced onion

Combine all ingredients in a jar with a tight-fitting lid and shake or put in a blender.