This is a translation error! The original French is as follows:
— Oh! monsieur, dit-elle, pourquoi donc êtes vous venu si tard aujourd’hui? Savez-vous que l’on va dîner bientôt, et qu’il m’a fallu bien de la diplomatie et bien de la promptitude pour me débarrasser de ma belle-mère qui m’épie, de ma femme de chambre qui m’espionne, et de mon frère qui me tourmente, pour venir travailler ici à cette broderie, qui, j’en ai peur, ne sera pas finie de longtemps?
Alexandre Dumas (1845). Le Comte de Monte Cristo, volume 7, p. 283. Paris: Pétion.
The French “belle-mère” means both “mother-in-law” and “step-mother”, and the anonymous translator of the 1894 Crowell edition picked the wrong one:
“And why do you come so late today? It is almost dinner-time, and I had to use no little diplomacy to get rid of my watchful mother-in-law, my too-devoted maid, and my troublesome brother, who is always teasing me about coming to work at my embroidery, which I am in a fair way never to get done.”
Alexandre Dumas (1845). The Count of Monte Cristo, volume 1, p. 516. New York: Crowell & Co (1894).
The mistake was corrected in the 1901 Crowell edition, which has “stepmother” on page 516, but Project Gutenberg used the 1894 edition as the basis for its e-book, and the mis-translation duly appeared in chapter 51 (but no longer; see below).
Another answer points out that “mother-in-law” can be used with the sense “stepmother” in English too, but this doesn’t apply to The Count of Monte Cristo, for the following reasons:
The Oxford English Dictionary marks this sense as “now regional”: that is, it is not standard usage, and so is the wrong register to represent the speech of Valentine, a member of the aristocracy who has grown up in Paris.
The fact that Crowell issued a corrected edition shows that they considered it a mistake.
The translator chose “stepmother” in six other places to refer to the relationship between Valentine and Héloïse, for example, this passage:
Elle extra donc, et voyant près de sa mère l’étranger dont elle avait tant entendu parler déjà, elle salua sans aucune minauderie de jeune fille et sans baisser les yeux, avec une grâce qui redoubla l’attention du comte.
Alexandre Dumas (1845). Le Comte de Monte Cristo, volume 8, p. 7. Paris: Pétion.
became, in the 1894 Crowell edition:
She entered the apartment, and seeing near her stepmother the stranger of whom she had already heard so much, saluted him without any girlish awkwardness, or even lowering her eyes, and with an elegance that redoubled the count's attention.
Alexandre Dumas (1845). The Count of Monte Cristo, volume 1, p. 526. New York: Crowell & Co (1894).
Accordingly, I submitted some errata to Project Gutenberg, and the six occurrences of “mother-in-law” in chapter 51 are now corrected to “stepmother”, following the 1901 Crowell edition.