There was nothing in the original letter to Prudie suggesting that the child was a discipline problem. Indeed, the woman's clear admission that the problem didn't begin until after she became pregnant with a child of her own strongly suggests otherwise. But even if the child were a discipline problem, hating her for it is neither a rational nor an adult response. Anger with the husband and his ex-wife for not instilling and maintaining some discipline might make sense, but loathing the child for having the unmitigated gall to have not been properly raised is cruel and despicable.
Yes, there are challenges involved with being a step-parent. I have three step-daughters and can attest to that. But I never for a moment hated them, even at the most difficult of times, nor did I ever have the immaturity to suggest that a child who has not been taught what the limits are is responsible for not knowing what the limits are.
If you cannot bring yourself to love the children of a prospective spouse, you have no right to marry him (or her). A parent's first responsibility is always to the children in his (or her) life. It's a package deal. Tolerating them is not nearly enough. They need kindness, consideration and love as well as direction and guidance. If you can't provide them with all of that, you have a moral obligation to restrict yourself to childless prospects for your future spouse.
Get some help or get a divorce. These children should not have to become the casualties of your own selfishness and jealousy.