Coraline's mom is a tricky character. We don't know much about her (including her name), which reminds us a little of the other mother. But that's where the comparisons to the other mother end. All we know about Mrs. Jones is that she's a distracted and busy woman who often ignores her daughter.
"But Mum, everybody at school's got gray blouses and everything. Nobody's got green gloves. I could be the only one."
Her mother ignored her; she was talking to the shop assistant. (3.5-6)
There's a definite distance between Coraline and her mom; she has a tough time getting through to her. In fact, this is what makes the other mother so dangerous: at first glance, the beldam is actually better than Coraline's mom. She gives Coraline every material thing she could want – new clothes, good food, a neat paint job in her room – and she pays attention to her.
But Coraline is wise enough to know that nothing can replace her real mother. Remember, when she needs some extra encouragement to get away from the beldam, Coraline hears her real mother's voice:
And then a voice that sounded like her mother's – her own mother, her real, wonderful, maddening, infuriating, glorious mother – just said, "Well done, Coraline," and that was enough. (11.39)
Like a lot of mothers and daughters, Coraline and her mom have some trouble understanding each other. But Coraline and her mom love each other, and the other mother can never compete with that.