Is it permissible to perform Salatul-Istikharah when supplicating sincerely and fearing that the response might not be good for the supplicant or their family, even though the supplication contains no sin or breaking of family ties?

Supplication (Du'a) is goodness and blessing, so long as it does not involve sin or severing ties of kinship. Allah grants the supplicant one of three things: He either hastens the fulfillment of their supplication, or He stores it for them in the Hereafter, or He averts from them an equivalent amount of evil. Supplication is worship. It is recommended to frequently recite the supplications from the Quran and comprehensive prayers for good, such as the supplication: "O Allah, I ask You for all good, both immediate and delayed..." As for Salat al-Istikhara (the prayer for guidance), it is performed for matters where the correct course of action is unknown, and it is not for supplication itself, as supplication is pure good.