Is it permissible for me to cut off my relationship with my wife's family to please my parents, or is it permissible for me to continue my relationship with them without my family's knowledge, and how do I balance honoring my parents with not wronging my wife?

Obeying one's parents and showing them dutifulness in what is good is obligatory. However, it is not permissible to obey them if they command one to abandon an obligation or commit a sin. Maintaining kinship ties is obligatory, and severing them is sinful. It is not permissible to obey parents in cutting off ties with the wife's family if there is a kinship relation. One must be kind to parents and treat them well, and alert them that forbidding this goes against the command of Allah the Almighty. The parents' command, even if it involves sin, does not diminish any of their rights. If parental satisfaction is impossible without them knowing that you have cut off ties with this family, one may resort to subtle hints [i.e., using allusive speech that conveys a meaning without stating it explicitly].