The house assignment for the mother arrives with the medieval catalogues and never fully settles.
The Hellenistic sources put both parents in the fourth. The fourth is the place of ancestry, the ground, the end of the matter and what lies under the native, and a single parental house serves a system that reads the two parents together as a sect pair. Lilly, writing in 1647 out of the Arabic and Latin tradition behind him, separates them. His fourth is the father's, and the mother appears in the tenth, listed among kings, princes, honour, office and trade.
That reads oddly to a modern eye, and modern practice usually inverts it, giving the mother the fourth as the house of home, roots and the private interior of a life. The inversion is now so common that it is often stated without qualification, and a reader who comes to Lilly afterwards finds the opposite in print with equal confidence.
There is a further route that sidesteps the argument. A derived house reading counts the mother's own chart from whichever house she has been assigned: her money is the second from it, her siblings the third from it, her death the eighth from it. The method is stable across the disagreement rather than settled by it. What it cannot do is tell a reader which house to start from, and that remains the question every practical reading has to answer before it begins.
Sources Christian AstrologyWilliam Lilly with Hellenistic Astrology: The Study of Fate and FortuneChris Brennan, The Contemporary Astrologer's HandbookSue Tompkins