Why would a woman regard it as important to have her children baptized and, if necessary, buried according to the rites of the Church of England? The background for this question refers to the Victorian age.

The answer to this question will differ slightly depending on whether you are referring to the early Victorian age or the late Victorian age. Queen Victoria reigned from 1837 to 1901, and this was a period of enormous change in Britain and across the world, particularly with regard to religion. While the Church of England had begun the era as the unquestioned dominant religion of England, by the late Victorian period, it had been wracked by the rise of competing faiths as well as the challenge of science, which had led some people to declare themselves atheists, something previously unheard of. At the beginning of the Victorian period, only somebody who had been baptized in the Church of England could hold public office or be elected to teach in the country's great universities, Oxford and Cambridge. By the end of the turbulent century, this was no longer the case.
Nevertheless, the Church of England remained of significant importance to the people of England and finished out the century as the dominant religion of the country—one inextricably linked to its power systems. The head of state in the United Kingdom, in this case Queen Victoria, is also head of the Church of England. In the Victorian period, this lent the Church a special credence not afforded to competing faiths such as Catholicism, Evangelicalism, Methodism and so on. Additionally, please note that Britain's first and only "Jewish" Prime Minister, Benjamin Disraeli, was baptized into the Church of England. If he had not been baptized, he would not have been permitted to serve.
Being baptized into the Church of England specifically, then, would have seemed necessary for any woman wanting to ensure that her children would have access to all opportunities throughout his or her life. The Victorians were generally religious and still largely believed that baptism and Church burial were necessary in order for people to be able to go on to an afterlife with God. Being baptized according to Church of England practices, however, meant more than this: in terms of life on Earth, it meant that the child would be viewed as part of the dominant group, rather than as an outsider, and that he could become a public servant or a university professor—that is, a respected person in society. The Church of England grew strongly during the Victorian period because a lot of money was invested in it, part of an attempt to expand its reach into the growing cities. Previously, traditional churches had been built in the villages out of which society was now growing. The rise in visibility of the Church, despite the equivalent rise of competitive forms of Christianity, would have reminded even those in urban areas that being baptized into the country's dominant church was still necessary not only to save a child's soul, but to save his or her social prospects.
https://www.english-heritage.org.uk/learn/story-of-england/victorian/religion/