What should I do about my half-sister, for whom I fear moral decay, given that I am unable to visit her for the sake of kinship ties or offer her advice due to my family's refusal, and no one from them is taking the initiative to solve the problem, contenting themselves with praying for her?

The Sharia commanded the upholding of kinship ties (Silat al-Rahim) but did not specify a particular method or extent for it. Rather, the reference for this is custom (urf). So, if it is possible to visit your sister without harm, then you must visit her. Otherwise, it should be done through communication and asking about her. It is not permissible to sever ties with her except with the intention of reforming her and deterring her from evil deeds. Among the greatest forms of upholding kinship ties is enjoining what is right and forbidding what is wrong for her. If she does not respond to advice, you must inform your father about her situation.