Ok well, Mrs Lyons employs Mrs Johnston to work for her.
Mrs Lyons can't have children, but Mrs Johnston (Known as the mother) has too many. When Mrs J finds out she is going to have twins she is upset as she can't afford them. Mrs Lyons persuades Mrs J to let her adopt one of the twins.
Mrs Lyons is very aware of her social and financial position and she uses it to influence Mrs J. (She offers to pay her for the baby at one point I think.) Mrs Lyons also comes across as very cruel and uncaring. She acts in a very formal way towards Mrs J and wants her own way. She is clearly desperate to have a child, and doesn't have any qualms about splitting the twins up, meanwhile Mrs J does. She is also quite conniving as she eventually tricks Mrs J into giving her the baby.
Mrs Johnston is the opposite in a sense as she is kind and approachable. (Despite the narrator calling her heartless at the beginning) She is frightened of Mrs Lyons as she is aware of her own position. (Socially, financially.) She is not very intelligent as she is tricked by Mrs Lyons. The mother is superstitious too, (this is shown by the shoes on the table incident) she also believes Mrs Lyons when she tells her that the twins will die if they find out.
Basically, Mrs Lyons is aware of the two women's positions and is cruel enough to use it to her advantage. She does not care for the mother, but cares about the baby very much. She just sees the mother as a way of getting a child. Mrs Johnston is frightened by Mrs Lyons, but trusts her. She just wants the best for her baby.
Sorry if that was a little vague, if you need anymore help feel free to mail me. I've probably forgotten some things; I haven't read the play in a while. Hope I helped!