I can’t speak for all cases, but in cases where the irreligious brother refuses to do chalitza, poskim have some very inventive ways of being matir the woman to remarry. They try to pasul the first marriage, relying on numerous sfekos, and some more radical poskim might advocate being mafkia the original kiddushin based on the fiction that she would never agree to marry the first husband if she knew how things would turn out (the latter is a very slippery slope). Money, of course is always used to entice the brother to cooperate.
If I recall correctly, in Ashkenazic communities, and many sfardi ones as well, a brother cannot opt for yibum over chalitza – yibum is simply not an option, and the bais din will exert proper pressure (similar to a mesareiv get) to get him to perform chalitza.