Does recording relatives to find out what they say about me, and severing kinship ties due to confronting them, necessitate sin?

You made a mistake by spying on your relatives based merely on suspicions. Spying is forbidden except to prevent an evil when a strong doubt arises. What is obligatory upon you is to repent to Allah for this spying and for the consequent severing of kinship ties. This repentance involves ceasing the act, regretting it, and resolving not to return to it. You should also seek forgiveness from your relatives if you do not fear a greater harm; otherwise, your repentance between you and Allah suffices. You have done well by maintaining ties with them and remedying the estrangement, so continue to do so.