The answer is no, at least in these fairy tales. You will never find a stepmother who welcomes a new bride into the household and says, "I'm so glad you married my son. Let's go get pedicures together."
For example, the stepmother in "The Twelve Brothers" is downright nasty: "After they lived together for a few years, the king's mother, who was an evil woman, began to slander the young queen" (The Twelve Brothers.35). This results in the maiden being sentenced to burn at the stake. The stepmother in a similar tale, "The Six Brothers," is even worse. Not only does she spread malicious rumors about the new bride, she actually steals away the newborn babies and smears the maiden's mouth with blood, implying that the poor girl ate her own children. But hey, what's a little cannibalism between family?
Why all this nastiness? Well, it's partly an issue of limited resources. If there's only so much food to go around, you want your kid to eat. And if there's only one hot prince to go around, well, you want your kid to snag him. We see this in "The Three Little Gnomes in the Forest," when, after the heroine's dad remarries, "The woman became her stepdaughter's most bitter enemy and tried to think of ways to make it worse for her from one day to the next. Moreover, she was envious because her stepdaughter was beautiful and lovely, and her own daughter was ugly and gruesome" (The Three Little Gnomes in the Forest.46). Maybe part of the problem is also sour grapes; the stepmother doesn't have a lot to work with since her daughter's not so great, so she puts her energy into dragging down the more eligible heroine.
It must really suck to be the new woman entering a house and trying to set things in order, while simultaneously making sure your offspring is cared for. As with other elements in the tales, the prevalence of stepmothers reflects the reality of mixed families throughout history, since dying in childbirth was pretty common back in the day (it happens to biological mothers in "The Juniper Tree" and the current version of "Snow White," among others). Looked at from that angle, stepmothers are survivors: they're not gonna let the previous mother's whiny kid get in the way of their success.