How can one deal with the problem of the spread of ritual impurity (najāsa) in the house due to the family's, especially the mother's, lack of understanding of its concept, particularly when she washes menstrual clothes in a way that leads to the contamination of floors and shoes with impure water, thereby affecting ritual purity (ṭahāra) in the house? Is there a jurisprudential (fiqhi) opinion that permits leniency in this case?

The water from washing impurities is pure if it separates unchanged. The legal maxim states that certainty is not removed by doubt. Therefore, the default is that the water coming out of the washing machine is pure, unless its impurity is certain. Washing an impure item with water does not necessitate the impurity of whatever the water reaches. If you are certain of impurity due to a change in the water's color, then you must wash whatever it touched; otherwise, pay no attention to it.