All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
There is no objection in the religion against providing for your brother; rather, what your are doing is a good thing as an expression of gratitude for him. Verily, these are the manners of a noble person. It is also from the manners of the Prophet, sallallahu ‘alayhi wa sallam. ‘Abdullah ibn ‘Umar, may Allah be pleased with him, narrated that the Prophet, sallallahu ‘alayhi wa sallam, said, "If someone did you a favor, then compensate him; if you cannot afford to compensate him, then supplicate Allah for him until you believe that you have compensated him." [Abu Daawood]
Moreover, it was narrated on the authority of Jubayr ibn Mut‘im, may Allah be pleased with him, that the Prophet, sallallahu ‘alayhi wa sallam, said about the war prisoners of the battle of Badr, "Had Al-Mut‘im ibn ‘Adiyy been alive and interceded with me for these mean people, I would have freed them for his sake." [Al-Bukhari]
Ibn Al-Jawzi wrote, "The Prophet, sallallahu ‘alayhi wa sallam, specifically referred to Al-Mut‘im ibn ‘Adiyy in the hadeeth because when his uncle Abu Taalib and Khadeejah passed away, the Prophet, sallallahu ‘alayhi wa sallam, went to At-Taa'if, where he stayed for one month, accompanied by Zayd ibn Haarithah. When he returned to Makkah, he entered it under the protection of Al-Mut'im ibn 'Adiyy, so he wished to reward and compensate him for his help and support if possible."
You are not obliged to ask your brother to work; however, someone else should advise him to work and earn a living so that he would not be a burden on you. Islam urges the Muslim to work and earn a living. There are many religious texts that indicate the virtues of working and earning a living. Allah, The Exalted, says (what means): {And when the prayer has been concluded, disperse within the land and seek from the bounty of Allah, and remember Allah often that you may succeed.} [Quran 62:10]
Moreover, Abu Hurayrah, may Allah be pleased with him, narrated that the Prophet, sallallahu ‘alayhi wa sallam, said, "By Him in Whose Hand my soul is, it is better for anyone of you to take a rope and cut the wood (from the forest) and carry it over his back and sell it (as a means of earning his living) rather than to ask a man (for money) and that person may or may not give him." [Al-Bukhari and Muslim]
Ibn ‘Umar, may Allah be pleased with them, reported that the Prophet, sallallahu ‘alayhi wa sallam, said, "The upper hand is better than the lower hand." [Al-Bukhari and Muslim] The upper hand is the one that gives, and the lower one is the one which receives.
Your wife has the right to ask for her financial maintenance if you fell short in providing for her. However, she has no right to prevent you from providing for your brother or anyone else. The husband's wealth is his own personal property; he is entitled to dispose of it as he wishes in the lawful ways, one of which is providing for his family in order to uphold the ties of kinship. The wife should help her husband accomplish this objective; this helps her win her husband's appreciation and respect. It also helps her observe the enjoined kindness and good companionship and foster love between them.
If your wife speaks ill of your mother and brother, then that is a serious misdeed. You should kindly advise her in this regard as well as clarify the importance of guarding her tongue and the gravity of speaking ill of people, cursing, and harming them. ‘Abdullah ibn Mas‘ood, may Allah be pleased with him, narrated that the Prophet, sallallahu ‘alayhi wa sallam, said, "The believer does not slander, curse, or speak in an obscene or foul manner." [Ahmad and Abu Daawood]
Allah knows best.