What do you mean by "well received"? Whether the minor character's POV will disrupt the flow of the story?I think it can work to enrich the story. The timing will be important--obviously you don't want to stick it in in the middle of some action scene. Also, I think it would need to address some question the reader has in their mind as they're reading the story, such as, why is the young MC so sensitive about her mother? If, then, the minor character has that perspective, the reader will be eager to encounter it and it will fit right in.
Books that come to mind are Barbara Kingsolver's Animal Dreams--it's written in first person except for one chapter, which is written in the MC's father's POV--and Gregory MacGuire's Mirror, Mirror and Wicked, in which he switches POVs to minor characters as necessary. Of course, these are both books. I don't know how different it would be with a novella. Short stories, obviously, would be more difficult.
I hope this helps. Really, I think you just have to try it, and if it doesn't feel right try it differently. I think it can work though.
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