Is it permissible to distribute the inheritance among the Muslim children of the deceased whose mother converted them to Christianity, bearing in mind that the daughter (17 years old) says she does not follow any religion, and the son is 16 years old?

The disbelieving son and the disbelieving daughter do not inherit from their Muslim father, based on the Prophet's (peace be upon him) saying: "A disbeliever does not inherit from a Muslim." The scholars have unanimously agreed on this. However, judging your brother's son and daughter to be disbelievers requires the verification of conditions and the absence of impediments. The mere writing by their disbelieving mother that they are Christians is not sufficient, nor is your testimony that the daughter admitted to disbelief acceptable, as you would be gaining a benefit for yourself. Therefore, the matter must be referred to a Shariah court, and the default is that they are Muslims. It is important to focus on inviting them to Islam more than on depriving them of inheritance.