Following the "golden age of domesticity", the social power of the housewife had to fall, as there was nowhere to go but down. I don't think it's possible to separate out the effect of the increase in automation from the other aspects of the trend, but it certainly played a part.

Through the seventeenth century and most of the eighteenth in Britain and America, housework was seen as something that simply had to be done and was relegated to the female side of the household, who generally trained from a young age in these tasks. In a family, there was a strict hierarchy based on gender, age, and class - the husband was superior to all; the wife was subordinate to him but superior to children and servants, etc. - that was seen as a microcosm and foundation of society. While women were below men, they were not actually seen as that different from men of their own class: an elite woman was far above a man of a class beneath her, and while she was supposed to be modest and obedient to her husband, he was supposed to be respectful and kind toward her. This subordination was largely due to biblical strictures of wifely submission - it was right and correct that husbands and wives/men and women act in this way because God ordained it.

In the very late eighteenth century, however, this society was beginning to see women's restriction to the private sphere as something inborn, almost scientifically justified by their femininity. Nature made it so only women gave birth, which must mean that motherhood is a woman's highest calling; nature made women physically weaker and quieter than men, which must mean that they're meant to stay indoors. Parents were supposed to be openly affectionate to their children in general, though they were still to discipline them when necessary, but women in particular were to devote themselves to the education of sons and daughters to produce good citizens and future wives. And of course, the concept of the home changed from a relatively private place to live to a warm, welcoming nest for husbands to come back to and children to leave - the "cult of domesticity". In this atmosphere, it became morally important for a woman to not just be competent, but perfection itself, when it came to cooking, cleaning, sewing, child-educating, etc. (or in managing others who did it for her, if she were affluent enough to have a maid, cook, nursemaid/governess, etc.) and to love doing it. While this is often seen as a primarily middle-class phenomenon, it still played into the negative judgment of poorer women if they seemed to be negligent in the home, but also positive judgment, if they overtly loved and sacrificed for their children, and the assumption that women all had wells of maternal feeling could help them in court cases and the public eye.

During the Golden Age, a housewife's abilities to make a cake rise, to cook meat so that it was neither raw in the middle nor overdone, and to remove stains from white leather were prized because they represented hard-earned skills. Novels featuring lavish descriptions of girls learning to enjoy housework were written, didactically informing the reader that frugality was better than lavish spending, and that cleanliness and order were better than fashionable disarray. This ideology was not just aimed at women, to emphasize what their role should be, but also at men, to teach them what to look for and appreciate in women. It was also possible for women to extend the concept of "raising children in a good home" to wider society by seeing to the education of working-class girls in domestic arts to prepare them for domestic service and/or motherhood, by performing charitable works for poor families, and by pressing for a better society (for instance, joining the Women's Christian Temperance Union).

Throughout the nineteenth century, however, inventions were being invented and developments developed with increasing speed, many of which eroded the amount of skill and practice required to do these things. For instance, baking soda/sodium bicarbonate was being produced commercially from the second quarter of the century: with it, any housewife could make a cake rise without having to beat egg whites by hand to the proper degree of frothiness. Comprehensively-labeled commercial cleansers and medicines were being produced that required women to think less about the mixing of potions or choosing which ingredients were useful for which issues. For more affluent women, it was easier to leave these things to servants without much supervision; for ones who still had to do this work themselves, it failed to reflect as well on them to be able to do it. The domestic science/home economics movement was born out of the Golden Age's approach to domesticity - broadly speaking, it was about making sure that all women were good at cooking and housework based on rational scientific principles - but it helped to bring it to a close by sucking the personal touch from domestic work and denigrating the "amateur" housewife, who did not know said scientific principles, and the traditional crafts of the domestic woman. They literally taught that food should not be enjoyable, but only fulfill the eater's caloric and nutritional needs. Why use fatty, animal butter when sanitary, healthful Crisco/oleo/margarine was found on grocery shelves? Why judge between different milkmen's wares when powdered milk will always be the same?

The turn of the century saw the introduction of frozen/canned food, and an explosion of premade ones cooked industrially, or sold as mixes (particularly during WWII), and sold under brand names across the country. Advertising would boom in the 1920s, informed by instructional texts that dismissed women's intelligence even while it acknowledged them as the most important consumers, as would electrification and the use of the installment buying that made it easier for housewives up and down the social scale to have machines at home to blend and iron and wash. Additionally, mass media and fiction generally chose to glorify the fun life over the domestic one, and the new dating culture allowed youngsters to escape maternal protection and guidance. Housewives were by this point not just seen as incompetent amateurs, but millstones on their financially supportive husbands' necks, and bores to their children. It was understood that a wife and mother was responsible for the happiness of the home still, but her position was no longer high enough to command respect and obedience, and doing anything but adoring and listening to her husband was impertinence or even destructive behavior. In a fully industrialized society, the non-productive work of maintaining a home was valueless. Using the language/stance of trying to make a domestic imprint on society as a whole, extremely common to women's activism in the previous century, was rejected, as was any expertise on the part of older women. By the pinnacle of this new form of domesticity in the mid-twentieth century, the ideal housewife cared about nothing but tending to her beauty and following the orders and desires of her family. Automation meant that she could do this more easily, since the washing machine and dishwasher would take very little of her attention (and not harden the skin of her hands).

Again, I realize that I've talked about a lot of things rather than just automation, so if I can clarify anything here for you, I'm happy to try to do so. The rise of household appliances helped to decrease the value of women's labor, but only after people were already beginning to doubt the value of that labor. This devaluing does also seem to have affected women's perception of their own labor, adding to the alienation of housewives that eventually led to The Feminine Mystique - it seemed to be pointless drudgery, something that completely bored an intelligent woman and wasted her life. But again, that's not just because appliances made that work simple, but also because their whole society told them that they were contemptible for not working (while also pressuring them not to work outside the home because then everyone else in the home would be inconvenienced).

You might be interested in "Just a Housewife": The Rise and Fall of Domesticity in America, by Glenna Matthews. It's all about this story, and a very good read.