Is the questioner considered a disobedient son, and is he sinful for his father boycotting him, after he refused to bear the expenses of his half-brother and took responsibility for caring for his mother and sisters?

If the father is angry and severs ties with his son because the son refrained from spending on his brother, then the father has no right to do so; for the financial support of a poor brother is obligatory upon his wealthy father. If the severance of ties is solely from the father, then there is no sin upon the son, and he is not considered disobedient, but he must strive to mend ties with his father and appease him as much as possible.