What should one do regarding a niece's theft, given that there is proof, yet legal action is refused out of consideration for kinship ties, even though her mother is hostile despite this?

Theft is a grave sin. If it is committed by a nephew/niece, it adds to the crime of severing kinship ties. The duty is to advise the thief to repent and return what was stolen. You have done well by not escalating the matter to legal authorities, and you have the right to forgive him/her. We advise you not to connect your sister's actions with the theft, and to strive for reconciliation between you, for kinship ties are great. If she continues to fight you, be patient and treat her well, even if she acts poorly.