Hopefully this is the right place.
First you should not say how a melusine could do this or that. Melusine (Mélusine, there is a accent on the 'e', pronounce that like may) is a name in the same range as Medusa, Zeus, or Barrack Obama. So simply Melusine.
She appears in lots of story, But the "Roman de Mélusine" by Jean d'Arras is the best representation.
Roman de Mélusine, jean d'Arras
Mélusine is known from this French middle medieval book. Here is a very short summary, with original quote and personal English translation. King Elinas of Albany (ie. Scotland, not modern Albany) meet an incredibly beautiful woman Présine and marry her at the condition he never comes to see her after child birth.
Old French text:
Dont, dist la dame, qui bien savoit qu'il estoit espris de s'amour:
Se vous me voulez prendre a femme et jurer que, se nous avons enfans
ensemble, que vous ne mettrez ja peine de moy veoir en ma gesine, ne
ne ferez par voye quelconques tant que vous me voiez, je suiz celle
qui obeiray a vous comme loyal moillier doit obeir a son espoux. Et le
roy lui jura ainsi.
So, says the woman, who was knowing pretty well that [Elinas] was in
love: If you want to take me as a wife and sear that, if we have
children, that you will not come to see me while I am giving birth, I
will be the one who will obey to you like a loyal wife should obey her
spouse. And the king sweared.
Note also that this 'de moy veoir en ma gesine" could also safely been translated by "When I have my period" which would make sense with the child bathing scene (could I insist).
Unfortunately the King has already a son Mataquas which is obviously jealous. Présine got pregnant from THREE girls at the same time. And following Mataquas advice the king go to see his wife.
Il s'en vint devers le roy son pere, et lui dit: Ma dame la royne
Presine, vostre femme, vous a apporté les trois plus belles filles qui
oncques feussent veues. Sire, venez les veoir.
[Mataquas] comes to the King his father, and says: My lady the Queen
Présine, your wife, bring to you the three most beautiful girls never
seen. Sire comes to see them.
One of this 3 girls is Mélusine. So you have to note that she is the daughter of a man (a King), and a obvious fae Présine which is pretty much female in appearance. The two other girls are Mélior and Palestine.
When they grow older the 3 girls decide to take revenge on their father, locking him in the Northumberland mountain. Présine, curses them for that. And here e have the passage answering your question:
Mais desormais je te donne le don que tu seras tous les samedis
serpente du nombril en aval. Mais, se tu treuves homme qui te veuille
prendre a espouse, que il te convenance que jamais le samedy ne te
verra, non qu'il te descuevre, ne ne le die a personne, tu vivras
cours naturel comme femme naturelle, et mourras naturelment.
But for now, I give you the gift that every saturday you will be a
snake from the navel to bottom. But if you find a man who which to
take you as a wife, that he promises you that he will never see you on
saturday, neither he finds you, nor he says to anyone, you will live
normally as a normal wife, and die normally.
So Mélusine state is the result of the curse of her own mother Présine, changing her on saturday to have sought revenge on her father. Her sisters are also punished.
She will spouse king Remondin (or raimondin, modern Raymondin), who will obviously comes to spy her (after an advice of his very own brother mentioning she could betray him) on a saturday and tells what he saw, obliging Mélusine to flee.
Here is Remondin spying Mélusine while she is bathing:
And Mélusine flying away as a monster after her betrayal (the text is: How Mélusine fly from Remondin in the shape of a snake of the castle of Lusignan by a window) - I picked this one cause it is totally ugly (drawn by a 2 years old monk):