Is discussing with one's husband his desire to reduce the time spent with his family considered backbiting (gheebah), and would this contribute to his disobedience (ʿuqooq) towards his mother, or is it a sin if the wife requests not to host his family at certain times?

There is no objection to advising the husband and consulting with him to organize the times of his family's visits, especially given their frequency. He can visit his mother in her home. It is not permissible to mix with his brothers except by adhering to the Shariah-compliant regulations, and the husband should not allow them to visit frequently due to the embarrassment and restriction of the wife's freedom that this entails.