What is the ruling on supplicating for the abandonment of one's family members for someone who believes that staying with them causes him psychological problems and hinders him, especially since he knows the Hadith: "If I were to supplicate for cutting ties of kinship, it would not be answered"?

It appears that the matter is exaggerated, and perhaps there are misconceptions on your part, especially concerning the relationship with your mother. Living separately from one's family after marriage does not necessitate estrangement. As for supplicating for the abandonment of family and the severing of kinship ties, this is impermissible and falls under the category of aggression in supplication, which is forbidden. It is included in the Prophet's (peace be upon him) saying: "The supplication of any one of you will be answered as long as he does not supplicate for a sin or for the severing of kinship ties." The remedy for what you complain of is not limited to this supplication. Rather, supplicate to Allah for well-being from all evil, and supplicate for your family for guidance and success.