I can’t answer this in character, because Catelyn wouldn’t answer it. She would think the question out of order, and the subject too painful to discuss with strangers (she barely discusses it with family. However, I can tell you her thought processes.
Firstly: Catelyn does not hate Jon. She dislikes him, she resents him, she fears him, she hates seeing him, but she does not hate him. He is no true relation to her, her children love him, and so she doesn’t hate him, she hates what he reminds her of, what he represents. But it’s mostly resentment she feels, which, while it can look much like hatred, is quite different.
Secondly, Catelyn was married to Ned and was to spend the rest of her life with him as Lady of Winterfell, giving him heirs, running a castle etc. Catelyn never hates Ned for sleeping with another woman, she doesn’t even feel hurt by it. She says herself that they had only known each other two weeks before he left for his war, that she knew men had needs, she had not expected him to be faithful and she was more concerned with little Robb. She didn’t really have concerns about the fidelity of a husband she barely knew. Therefore, there isn’t hatred at all there for that (although as she falls in love with Ned, there is paranoia/fear there, that he loved the woman more than her, but that’s a separate issue to this one). She was raised knowing men tend to Father bastards, and she says she could have forgiven Ned a dozen if they were out of sight. Her hatred for the situation comes from the fact Jon is allowed to live in the castle, is raised like a trueborn and made equal (in many ways, and especially in Ned’s eyes it seems to Catelyn) to her trueborn children.
Thirdly, Catelyn is smart enough to recognise that in those early days of marriage, if she hated Ned or resented him for Jon Snow, their marriage would never flourish, and while she never expects the deep romantic love they get, she does know that friendship and closeness will make the marriage, and thus Winterfell and their position, stronger. She puts aside her resentment towards Ned in this regard for the good of Winterfell, and for her duties (Family, Duty, Honour after all), and as they fall in love and have many more children, this obviously becomes easier and easier. She is, at first, forced to forgive Ned for the sake of duty, but with love it becomes a choice.
Fourthly, So she has to put her resentment somewhere. She doesn’t know who Jon’s Mother is, for if she was alive and Catelyn knew her (I mean I believe he is Rhaegar/Lyanna’s son, but I’m answering this from Cat’s perspective that it’s Ned and another woman) she would have placed a good portion of her resentment on her. But we only have Jon. So all these feelings Catelyn is forced to repress for the sake of duty fall on Jon. Now, let’s remember that in the world of Westeros, their politics, morals and societal rules are different to ours. Catelyn would have been perfectly in her right to have Jon taken away, many bastard children are left to die in the snow, and Cersei orders all of Robert’s bastards killed (Which people seem to forget when they attack Catelyn for her attitude towards Jon Snow), yet Catelyn does not. Catelyn (reluctantly) accepts Jon in their home (because she could have made enough of a raucous, she could have demanded he be gone, she could have done any number of things to force Ned to take him away, but she doesn’t), she doesn’t go out of her way to injure him, instead choosing to ignore him, leaving parental attentions to Ned, she never forbids her children from playing with him, she never turns them against him, she freely lets them love him like a brother.
Fifthly, Yet imagine how this makes her feel. In regards to Jon Snow, Catelyn is totally alone. Everybody loves him but her, she is alone in her resentment, alone in her pain there. Catelyn knows in the past bastards have killed trueborn sons in order to take the inheritance themselves; she fears Jon will one day do this. Jon was Ned’s first son, thus taking away her rightful duty. He looks more a Stark than her trueborn sons. He seems to find favour with Arya while Catelyn grows more distant from her despite her efforts. All her sons look up to him, Ned will hear no word against him. People whisper constantly about him, they whisper about his Mother, and they whisper that Catelyn is weak to allow Jon to stay (even Cersei presumes Catelyn must have been weak to permit a bastard in her home, as Robert tried to bring a daughter home once and Cersei threatened to kill her if he did), but she can’t complaint to anyone about this, or confess any of her fears…she is entirely alone. And Jon Snow is the cause, and so she resents him. The resentment grows, he is the thorn in her side that never leaves, the dagger that continues to twist.
In conclusion, Catelyn cannot hate Ned instead, because she doesn’t hate Jon. She resents all the feelings it causes, all her fears and worries, and Jon is the cause of them by being born.