I agree with the comments that there is no insult or disrespectful term specific to parents. I know some American kids who, when angry or frustrated with their parents, will call them by their first names, which is only mildly taboo but not common. More common culturally would be generally disrespectful sounds or gestures - eye rolling, slouching, not making eye contact, stomping their feet or slamming doors, making huffing or whining sounds.
In extreme cases of disrespect, a child might "flip off" or raise their middle finger to their parent. This is the equivalent of saying "fuck you" and considered highly inappropriate for children/young teens to be doing. Similarly, a very disrespectful child might call a parent swear words like "bitch" "cunt" "asshole" or "fucker." But most of society would view something as deeply wrong there. While these words come from sexual roots, there isn't a strong sexual context anymore, so they are inappropriate to say to a parent because of general respect, not because of sexual implications.
There are also class-based, region-based, and race-based differences. In general, there is a reputation of white kids as more disrespectful to their parents than most other races in the US. But even as a child who grew up in mostly-white areas, I don't think I ever heard or saw a child actually swear at their parent.
Frequency of Address
One possible cultural difference - English speakers often just address people as "you" especially in informal settings. So if we imagine an argument between a parent and child, it's likely that the child wouldn't address their parent as anything specific at all. For example:
Mom: "Your room is a mess! You cannot go to the party until it's cleaned up. How did it even get like this?"
Child: "Ugh, it's fine. It's my room anyway, why do you even care?"
It's fairly common for a child to only address a parent as Mom/Mum or Dad if they are trying to get their attention or in a setting where they might be talking to someone else. In situations where two people are only talking to each other, using someone's name or title is rarer and implies a sense of either formality or importance to the situation.
Nasty as an Adjective
As an aside note - in this question, you used the word "nasty" to refer to a child as bad, disrespectful, or naughty. The word nasty can mean "bad" or "cruel" but it can also mean "dirty" (either physically dirty or in a sexual way). To this American, calling a child nasty seems a little strange in this context.
I might call a child "nasty" if they were:
- Cruel or mean to other children, those they had power over - As a synonym for being a bully.
- Covered in dirt or mud or some other gross thing.
In this case, I would say that you are talking about a child who is rude (as an informal word) or disrespectful (as a more formal word). I believe in the UK, they may use the word naughty to describe a child who behaves poorly, but that is not common in the US.