"Your wit never ceases to underwhelm me."

Cousinly rivalry that goes further than it should, seeing as their mothers have little-to-no contact,

She and Demelza have a. . .rivalry. Never mind that they barely knew each other in Hogwarts, or that there's four years between them. Desmelda hates Demelza, and Demelza hates Desmelda.
Desmelda is the oldest daughter of Vania Carrow (née Avery) and Pylades Carrow. Melza's mother Anne was supposed to marry him. . .but then she ran off with Melza's father, and Vania married Pylades in her sister's place.
Desmelda has a sister (Melantha) eight months younger, and they're often mistaken for full twins, rather than "merely" Irish twins (much to Flora Megaera Carrow 's displeasure).

Desmelda is . . . basically, she's everything that Demelza's mother wanted her to become. Well-mannered, well-bred, well-read, lovely, married well, good family, three perfect children, all those white-picket fence. Also because of this, she has a solid dislike of Demelza who is. . .pretty much the opposite of that, and the two might somehow be found clashing at Hogwarts (despite Desmelda being four or so years younger).

She married as she ought to, and timed her children's births to interfere the least with her ballet career. She's a very talented soloist. Twins run a fair amount in her family, so no one was really surprised when she gave birth to fraternal twins.

Melza is convinced that the sole reason Desmelda took her husband's name was to be the better known De_mel_a Ro--.

Melza's mother is also convinced that the similarity of names was a direct insult. (As it's an Avery custom to name relatives slightly after each other, it's saying Anne is forever connected to them, there's nothing she can do about it, and a sort-of obviously you're still one of us, you named your daughter after someone, and you're not creative either.) It's definitely not an olive branch, as both sisters know perfectly well that's the last thing Anne wants.
-- Desmelda might also think similarly, which is another reason she could dislike Demelza. I mean, really, being named after your cousin? Your half-blood disgrace of a cousin?

Husband: Aelius Rookwood.

Children: Octavius (2010), Julianna (2013), and Typhaon (2013).

Avery jawline, but not the Avery coloring-- that's not too present in their line. Her mother had brown hair, her father blonde from his Greengrass mother. She's second cousins with Carrow twins 2.0, and the Bulstrodes.

She gets along fairly well with OG Carrow twins, and Carrow twins 2.0, for all that she's not quite as bloodthirsty as them, though she is, of course, a purist.