Is accusing relatives of stinginess and miserliness a sin after reducing communication with them and refusing to meet their increasing demands for money and gifts, despite continuing to give charity on occasions, and after verifying that they are not eligible for Zakat?

There appears to be no sin in what you have done. Setting limits on your interactions with your relatives, without abandoning them or cutting ties, is permissible. Maintaining ties of kinship means treating them well, as is customary. Assistance is not obligatory; if you donate, you have done well, and if you refrain or donate according to your ability, there is nothing held against you. We advise you to treat them tactfully to preserve harmony, and to beware of Satan’s entry to distance hearts and sow enmity and hatred, for the Sunnah (definition) has shown Satan’s eagerness to create divisions among people.