How is Addie's maternal influence on the children different from Anse's paternal influence on the children in As I Lay Dying?
The way this question is posed presents a bit of a conundrum. In the novel, both Addie and Anse are largely passive and absent as parents in terms of modelling behavior, providing affection, and offering a connection with their children. Anse's lack of positive parenting is rather well matched to Addie's selfish and isolated mode of being.
While Anse conducts a life without sweating (in a climate where this requires somewhat extreme measures of dedicated sedentary behavior), Addie simply does not like her children. Jewel is the only child that Addie shows real affection for.
In the action of the story, Addie is not a character so much as she is a presence. Unable to move or speak, she enacts the novel's title, effectively, and provides the impetus for the family's quest after she dies. In her capacity as a "presence", Addie can give no solace to her children and no maternal affection or care.
For their part, the children do not seek much affection from Addie. Darl feels connected enough to his mother so that eye contact suffices between them. Dewey Dell takes over the burden of "mothering" the family, to some extent, which means she is tasked with fanning her mother. Vardaman and Cash each lay their work in front of Addie's window, attempting to please her. Addie turns her head away.
While she once felt happy in her life with Anse, this has not been the case for a long time.
Considering Darl, Dewey Dell, and Vardaman products of an unhappy time, she does not feel affection for them...
This summation of Addie's behavior in the novel is also, necessarily, a summation of her style of maternity. The family tends toward isolation, as Addie did in her life. This seems to be her legacy, though it is difficult to see any maternal feeling in it.
Addie, however, does not betray her family outwardly. Anse does.
While in Jefferson, he takes Dewey Dell's money, buys false teeth, and secretly woos a local woman.
Treating his family as a resource or, perhaps worse, as a collection of people who owe him something, Anse feels no compunction about acting selfishly. He often says that he is engaged in a maximum effort.
"I do the best I can, much as I can get my mind on anything..."
His claims of suffering and payment are primary parts of his character, serving as his refrains and his constant excuse not to actually do any work. Similar to Addie's legacy, Anse's paternal influence seems to communicate an idea to his children that they have to fend for themselves. No one will protect them. Anse has already done all that he can do, for himself or anyone else.