Unlike others in this thread, I'm not necessarily a Karna fan (my favorite character is Bhima). But I did take your thread to be more about Kunti, and on her, I happen to consider her one of the most loathsome characters in the epic, rivaling Manthara in the Ramayan. Yeah, I agree that Karna had his faults, but all that is tangential to the question of whether Kunti did right by him.
I agree w/ RkS above that she didn't ask him to spare any of her sons, but disagree w/ her that she had the 'maternal license' to ask a son she had either forgotten or ignored all those years to now turn around against the person who made him what he was. If she didn't like the idea of her sons killing each other, she should have introduced them to each other before. After the game of dice, things were simply irreconcilable. And if her sons didn't kill each other, they did freely kill her grandsons - Karna Ghototkach, and Nakul, Arjun and Bhima all but one of Karna's sons (who was killed by Satyaki)
Even if one accepts that she was shocked at the archery contest, she had a number of opportunities where she could have told her sons about Karna - after the house of lac, during the Pandava reign in Indraprastha, and similarly, she could have invited Karna and instead of doing it during his pujas, invited him to a private setting and told him their whole story. B/w Karna and Yudhisthir, they could have worked it out.