Is it permissible for the wife to sever ties with her family if they interfere between the spouses in a way that could lead to divorce, especially if she responds to them, and if not permissible, what is the permissible extent of the relationship?

If you are able to combine maintaining kinship ties with fulfilling your husband's rights without negative influence from your family's words against him, then this is better. However, if you fear your family's influence on your relationship with your husband, which might lead to unlawful actions such as disobeying him or seeking divorce, then limit your kinship ties to the obligatory extent.