What is the ruling on a mother sitting at home in revealing sleepwear in front of her children (a boy 4 and a half years old, and a girl 3 years old)? Is there any educational harm in that? And when is that permissible or not permissible? Is it permissible for the boy and the girl to bathe together at certain times due to the mother's limited time?

The ruling on a mother exposing her body in front of her children varies based on their discernment (tamyiz). If a child is below the age of discernment, there is no harm in the mother showing some parts of her body in front of them, but it is more cautious not to accustom them to this.

As for a discerning child who has no sexual desire, their 'awrah is the area between the navel and the knee. For a discerning child who has sexual desire, a mother should not expose anything to them except what is normally shown by a woman in front of her mahram relatives, as a form of upbringing in accordance with Islamic etiquette.

It is permissible for boys and girls to bathe together at a young age due to the absence of 'awrah. However, they should be separated at the age of seven, especially when bathing, to accustom them to proper manners. Parents must raise their children with Islamic morals, especially in this era where vice has become widespread.