Mrs. Dubose is a haggard, two-faced old nag who bullies little children because she can; and then when it suits her, she turns polite for Atticus because he's respectable and kind. However, that does not stop her from gossiping behind his back and calling him terrible names. Mrs. Dubose tells the children that their father should have remarried after their mother died because Atticus just lets them run wild. She did, however, say that their mother was lovelier than any that ever lived; so it's a wonder why she would treat the children with such hatred and vice! Mrs. Dubose is mostly disappointed with the way the children, particularly Scout, run around getting dirty all day long. She also disapproves of the children calling their father by his first name and says they are disrespectful to do so.
Atticus, on the other hand, is always respectful, polite, and courteous to Mrs. Dubose. The kids are respectful and polite, as well, but Jem contradicts her when she is incorrect sometimes. But even then, that's no reason to completely hate the kids.
Another reason Atticus is treated better than the children is because it would be very difficult for any woman to be unkind to a man who does the following:
"Atticus would sweep off his hat, wave gallantly to her and say, 'Good evening, Mrs. Dubose! You look like a picture this evening.' I never heard Atticus say like a picture of what. He would tell her the courthouse news, and would say he hoped with all his heart she'd have a good day tomorrow" (100).
A lady, no matter how old, can't be disrespectful to a man who is so courteous in her presence. She eventually asked Atticus to draw up her will for her, which also put her on a more even playing field with him.
Finally, Atticus knew about her morphine addiction and that could have humbled her when she was in his presence. There's just something about showing respect for authoritative, but kind people like Atticus, too. Jem and Scout did their best to speak to her with the most kind words they could muster. Nevertheless, Mrs. Dubose treated them the way she must have felt about them. She had no filter and no guilt associated with telling children where they went wrong. But again, as it came to Atticus who was an established and respected leader in the community, she had to be nice to his face.