I just can't see Clownpiece as anything but Hecatia's daughter.
To each his own headcanon. The Lampades weren't Hecate's offspring in Greek Mythology, and I don't remember ZUN ever confirming that Clownpiece is Hecatia's daughter.
Personally, I like to interpret the dynamic between them as less "mother and daughter" and more "mistress and servant", in a vaguely-similar vein to Remilia/Sakuya.