An example-- Anne Boleyn was executed for adultery, incest, and treason when her daughter, Elizabeth I, was a little more than 2 years old. So as Elizabeth continued to grow older still surrounded by her father's court, was she taught that her mother was an adulteress and a traitor to the King? Did she regard her mother as a "bad person" who deserved her death?
In general, were noble or royal children in these situations ever taught anything about their parents and/or feel sadness for their loss? Or were they basically just considered part of the past with little to no regard at all?
It really depends on the situation.
Elizabeth is an especially difficult case because even for a monarch she is fairly inscrutable. For instance, we have no doubt about how Mary I felt about her mother. But for Elizabeth her personal thoughts were not recorded in any manner. And, in general, her public statements were often intentionally contradictory on just about any topic. She also loved to ignore unpleasant issues and was quite expert at doing so.
Elizabeth never mentioned her mother. Her public statements all indicate great love and admiration for her father. But, of course, he was where she derived her authority. She was also proud of being said to resemble him. She would have said and done what she had to to survive and thrive in his court. She also never had her mother reburied in ceremony (as James I did with his mother, Mary, after his succession.) She also never revoked the act making her a bastard and annulling her mother and father's marriage. Which Mary I did for herself. Mostly her public position was to ignore it.
That being said, she did promote Boleyn relatives at court and provided well for female Boleyns by arranging marriages. She possessed and kept through out her life some of her mother's jewelry and papers. She had a locket with her mother's image. She is known to speak with people who knew her mother to find out more about her. So, her private actions suggest some sense of loss and attempt at a connection. That being said, her feeling some connection with her mother doesn't necessarily mean she didn't think she was a bad person who deserved it. Again, she never made any attempt to rehabilitate her mother.
So, we just have no idea how she felt about her really. We do know that she obviously felt it was a topic best not addressed.
Generally, as I said, it depends in the circumstances. Edward III publicly "avenged" his father's death and honored his memory. At the same time, he remained close to his mother, who was at least partially responsible for the death, his whole life. After a brief imprisonment and having all her lands stripped from her she had a handsome allowance and was visited by her family often (although she did not come to court). His children were also close to her. So, the situation is as complicated emotionally as politically.
James VI and I was just an infant when his mother fled to England and he was raised by advisers largely hostile to her. When she was put on trial with the inevitable result being execution he didn't protest. He was always firm in his alliance with Elizabeth over any potential betrayal in favor of Mary. But, as mentioned above, he had her body moved to be buried in state (right across from Elizabeth, herself) upon his accession to the throne. There were also officially commissioned biographies redeeming her to a degree. Not completely exonerating her but casting her as more unlucky than duplicitous. So, in that case there was some connection to his mother and need to have her redeemed.
For non-royal but noble children the circumstances vary even more. The execution of a traitor didn't always mean the children were removed from the care of their mother or other relatives. So, their family could very well raise them to believe honor and love their parent. And they may have the ability to openly mourn. A man who was executed a traitor didn't always have a bad reputation after his death, either. As an example, Edward II executed Thomas Earl of Lancaster. But the titles were later restored to his family (a brother because he had no legitimate issue) and his verdict overturned by Parliament. So, his children (illegitimate) would have had vindication and reason to honor his memory.
Simon de Montfort's children always honored his memory and some sought to avenge him. But his youngest was 13 when he died and his eldest was an adult. So, they would be people with actual memories of the man, himself.
For the most part, it was a balance of political necessity and emotional reactions. The ability to act politically over emotional connection to a parent even in children shouldn't mean we assume they didn't have those emotions.