Is supplication sufficient to reconcile relations between a sister and her paternal half-sisters, given the impossibility of reconciliation due to the continuous problems from her sisters' side?

The Prophet, peace and blessings be upon him, forbade turning away from one another and cutting ties among Muslims in general, and especially among siblings. Their connection is obligatory, and severing ties with them is forbidden, even if they commit an offense. Their connection is obligatory to the extent that it does not harm the one connecting. Praying for their reconciliation is not sufficient; rather, they must be connected at the minimum level, such as by greeting them with peace (salam). If you are not cutting ties with them, but they are cutting ties with you, then you are not sinful.