It is clear that Beatrice uses a number of different ways to keep her power over her children, and above all else it becomes obvious to the audience that Beatrice is a character who has suffered greatly, and as a result of her suffering, takes it out on her two daughters. Note for example the way that she is constantly verbally abusive towards her two daughters. Consider the following quote:
Oh, you're sick all right, the exact nature of the illness not fully realised, but you're sick all right.
The reference to Tillie being "sick" is something that shows how Beatrice is a character who hurts those closest to her because of her own suffering. Note too the way that she refuses to let Tillie go to school, even when Tillie asks her, as she insists on her staying at home and helping out with tasks. Beatrice is likewise cruel in her relationship with Nanny, ridiculing her even when she is right in front of her. Beatrice therefore is a character who is extremely cruel to those around her, using her dominance to maintain her power and to try and prevent her children from making a success in their lives because she herself made such a failure of hers.