"Total Eclipsa the Moon" and "Butterfly Trap" established that Queen Festivia was unrelated to the Butterfly family, just an ordinary peasant baby, but "became" a Butterfly after she was given the Wand. She had no cheek marks as a baby, but was given the Wand when she was adopted and developed permanent cheek marks and magic.
Likewise, we now know that there was a male Butterfly Queen name Jushtin who had cheek marks, despite it being established that male Butterflys do not inherit cheek marks (e.g. Moon's brother Uncle Heartrude).
Female Butterflys inherit magical potential and cheek marks from birth, but it seems that anyone can "become a Butterfly" with enough exposure to and usage of the Wand.>>99813343
Lobster Claws only held the wand once and never actually used it.
Ludo's wand was broken, and it turned out that he was mostly just venting evil/corrupted magic from Toffee. Star's more complete wand also wasn't operating properly, for example not changing when people other than Star held it. It's possible that because of it being broken/cleaved, Star and Toffee were "locked in" to being the wand's "owners" so Ludo's half never even drew out Ludo's own power, it was just channeling Toffee's power/pulling directly from the Realm of Magic the whole time.