Is it permissible to give charity equal to the value of items taken by the sister from her relatives' house without their knowledge, or should she return them to her sister to dispose of as she sees fit, especially since she was unaware it was theft and fears being accused of stealing if she returns them hand-to-hand?

Theft is a grave sin, and what the sister was doing by bringing items from her employers' house without their knowledge is unlawful (haram). She must repent. The questioner must also repent for what she took from her, as it is consuming unlawful wealth. Repentance includes returning what was benefited from. It is not sufficient to give charity equal to its value as long as the owners are known. It can be returned by any possible means, such as returning it discreetly, or sending its value without mentioning a name.