I am wondering whether income from an internet café is halaal or haraam, noting that this café is the only source of income for a Muslim family.
The internet may be used for both halaal and haraam purposes, for both good and evil. If you can control the place and prevent people from using the internet in haraam ways, then the income that comes from this café is halaal.
But if the owner of the café is careless about denouncing evil actions of his customers and he does not prevent them from doing haraam things, then he is a sinner, because he does not denounce evil and he cooperates with them in sin. In that case his income is evil and is haraam.
See also question no. 34672
And Allaah knows best.