Am I obligated to visit my brother, who is ill with a dangerous and contagious bacteria, given a 50% risk of the infection transmitting to me and my child, or should I refrain from visiting to avoid that, especially since he is alone in a foreign land?

We have already clarified the permissibility of taking precautions against someone afflicted with a contagious disease. Indeed, Al-Tabari reported that 'Umar ibn Al-Khattab said to Al-Mu'ayqib, who had leprosy, "Sit away from me the length of a spear."

Therefore, what is prescribed for you is to take precautions against that. You can inquire about him while avoiding harm, such as greeting him without entering the isolation room. The specialist doctor should be consulted regarding visiting him. You should do whatever good deeds and maintain ties with him as much as you can, without incurring harm upon yourself, for "there should be no harm nor reciprocating harm."