Is my not communicating with my brother, his wife, and his children—due to their repeated harshness and their not responding to my invitation to my wedding—considered a severance of kinship ties?

Your brother and his children are among those with whom kinship ties must be maintained, and it is not permissible to sever relations with them under the pretext that they are not fulfilling their duties. For maintaining kinship ties is not a matter of reciprocating good deeds or tit-for-tat; rather, it is a command required of the legally responsible person, whether his relatives fulfill their duty towards him or not.