Is a person considered a severer of kinship ties (Qati’ ar-Rahim) if he cannot live with his parents to care for them due to his wife's refusal, coupled with his poor relationship with his siblings and his mother's marginalization of him?

Your duty is to be dutiful and caring towards your parents, especially in their old age. However, your wife is not obligated to obey you regarding living in your father's house, as she has the right to an independent and suitable dwelling. You can look for a residence close to them. Serving one's parents is an obligation upon all children. As for your siblings, you are obligated to maintain ties with them, even if they cut you off, as the Prophet, peace and blessings be upon him, said: "The one who maintains ties is not the one who reciprocates, but the one who, when his kinship ties are severed, reconnects them." This is unless maintaining ties with them causes you harm, or if cutting them off is to rebuke them for an evil. Islamic law does not specify a particular method for maintaining kinship ties; rather, the custom (Urf) is the reference for that. Among the greatest acts of dutifulness towards them is inviting them to Allah, advising them, enjoining what is good, and forbidding what is evil.