Is it permissible to undertake administrative adoption of my sister's two daughters, with everyone being aware of their lineage, in order to facilitate travel and movement for them, and to protect them from destitution after their parents' divorce and their mother's plan to marry her lover?

Adoption is forbidden due to its implications of mixing lineages, violating rights, and other prohibitions. However, if these prohibitions are avoided, and the matter is merely about official documents that facilitate the guardianship of the two girls, without any of the forbidden aspects of adoption resulting from it, and if leaving them unattached to the family would cause certain or highly probable harm to them, then there is no objection to that. This is especially true since the continued presence of the two girls with their mother would lead to their corruption.