About Lilian’s mother, perhaps we interpreted things differently but I personally felt that the husband made an effort as he put her name forward but the publishers forced him to remove it even though he pushed to have her name included. The mother started to become resentful and upset as things started compounding. Arnold, Lilian’s father, going first to Germany and choosing that over staying back with her, which she seemed to have demanded of him out of spite. He shouldn’t have left her still. His angry outburst when he was going ahead without her. This might come down to each reader’s personal views, but either the husband was not the strongest ally against the establishment as he caved too easily or that the establishment’s entrenched misogyny was too much for a single man to overcome. So the mother, Helena, lashed out at her husband.
She even has an affair and gives birth to another man’s child, Lilian, while Arnold is working in Germany. He actually sticks by his wife to protect her from greater society who would shun her for having an affair and raises the baby as his own. Ultimately sacrificing his life to protect Lilian.
It’s kind of tragic too that Arnold and Helena’s baby together, William, dies and the only one left is Lilian, the affair baby, but I guess part of the moral of the overarching story is not being bound to the sins of the past.