Even though motive does not prove guilt, it can be excellent corroborative evidence. Even though James's 1898 Turn of the Screw is deliberately ambiguous, the story can be interpreted as the machinations of the children and Mrs. Grose. In the 1961 movie The Innocents, directed by Jack Clayton, the actions of the children, Miles and Flora (Martin Stephens and Pamela Franklin) and Mrs. Grose (Megs Jenkins) become even more apparent. When the governess (Deborah Kerr) arrived, she immediately took charge of Bly. This might have led to resentment by the others. It would have been to their advantage to drive the governess away. While it does not prove anything, this plot is certainly a distinct possibility.
When the governess appeared at Bly, she wasted no time in taking subtle charge of the the children and the whole household, as she claimed that the uncle had told her to do. This had been the job of Mrs. Grose. Perhaps because the governess was more educated and more respectable, she felt it was her duty instead of Mrs. Grose's to keep the household in order. Therefore, Mrs. Grose would certainly benefit from getting rid of the governess. She would have profited from encouraging the governess' delusions concerning the ghosts. In fact, the governess thought the man in the tower (Peter Wyngarde) was just a trespasser until Mrs. Grose said otherwise, that he was Peter Quint, the late valet of the uncle. The governess would have thought nothing about it until the housekeeper implied that ghosts were at work.
Likewise, the children had free run of the house until the governess arrived. They also stood to gain from driving her away. It would have been so easy to play upon the fears of the already skittish governess. Children do play games, and the governess was an easy target for their scheming. While Miles died in the attempt, they did get rid of the governess.
Even though it is impossible to prove, Mrs. Grose and the children may have been trying to get rid of the governess. They certainly had the motive to do so. While the conspiracy was not entirely successful (i.e. Miles died), they did drive the governess away and ruin her future.