What is the ruling of Islamic law regarding dealing with a father who suffers from obsessive-compulsive disorder and orders his children to sever ties of kinship, and threatens assault if they do not comply with his commands?

Obedience to the father is not obligatory in severing ties of kinship. Therefore, one can maintain kinship ties without his knowledge. Maintaining kinship ties has degrees, including the obligatory (wajib) and the recommended (mustahabb), and their determination is based on common practice (urf). So, whatever people consider as maintaining ties is so, and whatever they consider as severing ties is so. Relatives are not all the same; maintaining ties with maharim (unmarriageable kin) is obligatory, while scholars have differed on the obligation of maintaining ties with non-maharim. Accordingly, it is possible to combine maintaining kinship ties with not angering the father, by maintaining ties with relatives to the extent that fulfills the obligation and absolves one's responsibility, without informing the father.