The search for a quote’s source lead me to an article from 1904 by “The Bachelor Girl.” The author had a longer excerpt of the quote:

By a girl, by a young woman, or even by an aged one, nothing must be done independently, even in her own house.
In childhood, a woman must be subject to her father, in youth to her husband, when her lord is dead to her sons; a woman must never be independent.
[...]
No sacrifice, no vow, no fast must be performed by women apart from their husbands; if a wife obeys her husband, she will for that reason alone be exalted in heaven.
A faithful wife, who desires to dwell after death with her husband, must never do anything that might displease him whether be be alive or dead.
[...]
Day and night women must be kept in dependence by the males of their families.

The clipped portions are arguments against the wife leaving her husband over various issues. You can read those from the full article if you are so inclined. So, any guesses on where it came from? The text sounds remarkably like what I read in Me? Obey Him? by Elizabeth Rice Handford (except about the woman obeying the man even after his death). You might be interested to learn that this quote came from the Hindu Code of Manu. The article went on to point out something else:

In the Representative Church Council of the Church of England recently a motion was made to allow women -- not to be delegates -- but to vote for the men delegates. Lord Hugh Cecil, son of the Marquis of Salisbury, led the opposition, on the ground that Paul excluded women from the deliberative functions of the early Church. Nevertheless, the vote stood 153 to 58 for the women. Paul seems to be getting more old-fashioned every year.

They have a point. If women cannot be trusted to lead, why should their voices be trusted in a democratic process?