Does impurity transfer from clothes wet with urine when they are worn by mistake, and is ghusl then obligatory?

Doubt regarding the transfer of impurity is not to be entertained, for the default state is purity and impurity does not transfer except with certainty. Therefore, your clothes do not become impure merely by doubting the transfer of impurity to them from your brother's wet clothes. Furthermore, concern about the location of your brother's urine and his clothes is a form of waswasah (whispers of Satan/obsessive thoughts) that should be disregarded.