Does my sister have a share in what my father left after his death, and does her marriage to a Christian or her statement about her children's freedom to choose their religion affect that?

The reasons for inheritance are: lineage, marriage, and clientage (wala'). Its impediments are: slavery, murder, and difference in religion. The sister's fleeing does not prevent her from inheriting unless she commits apostasy.

A Muslim woman marrying a non-Muslim is forbidden and null by the consensus of Muslims. If she knew of its prohibition and deemed it permissible (istiḥlāl), then she is considered an apostate. If she did not deem it permissible, she is sinful and her marriage is null.

The sister's statement that her children have the freedom to choose between Islam and Christianity is a false and grave abominable statement. If she considers her marriage to a Christian permissible, or deems their religion correct, or doubts their disbelief, then this is from the nullifiers of Islam.

In conclusion, the sister inherits from her father if she remains upon Islam and did not deem her invalid marriage permissible, nor deemed the religion of the Christians correct, nor doubted their disbelief. If she contravenes this, then she is an apostate and does not inherit.