Do you mean that you are embarrassed for someone else's parents rather than your own? In the sentence given here, the fellow is ashamed (not necessarily embarrassed) of his own parents. To be embarrassed for someone else, in a sort of empathetic way, would be "Hij schaamt zich voor de ouders van zijn vriend" Your sentence would be "Ik schaam me voor je ouders.". To be embarrassed is a bit difficult to translate. Sometimes it is schamen but sometimes it is expressed in other ways. But the voor is what seems to have caught you. It would be okay in English as well, "He was ashamed for his parents" but it is a bit old fashioned. Keep in mind that Dutch is one of the closest languages to English but sometimes you need to reach back to your Shakespeare to get the connection and the two languages have obviously diverged a great deal, so it doesn't always help to remember this.
I am confused by what could be two different meanings. 1. He is ashamed of his parents - the parents have done something shameful. 2. He is ashamed for his parents (for his parents' sake) - the son did something shameful. Imagine that his parents gave a party and he did something stupid in front of his parents' colleagues: he is not really ashamed, not knowing the guests, but feels compassion for his parents' shame. Are both expressed the same way by 'voor zijn ouders'?
"He is ashamed for his parents" like "he is ashamed of his parents" describe his parents as the source of shame. While both infer that his parents may or may not be aware and both infer that the shame may be legitimate, only the former infers that that his parents may share in the shame. Such is my reasoning that both translations to (American) English should be accepted
Sounds like you have a typical teenager in mind. No, just as in English, you need to give a bit more information to clarify the reason for his shame, so you would say, "Hij schaamt zich in de aanwezigheid van zijn ouders.", which really doesn't explain why he's ashamed, just that he's ashamed in the presence of his parents. That would be pretty spot-on for most teenagers, since they don't know why they are ashamed or embarrassed of their parents, they just are.