Dear sister, you can only control yourself, order those you are authorized over, and advise those around you. Always think in these three levels: You have no control over anyone except yourself. You can only decide what you do and nobody else, so always make sure you do the right thing for you, and let people be people. As for those you control, those are your children, not your sister or parents. you order your children and they will listen and if they don't, you have the hadith of the prophet to guide you regarding teaching them and beating them if they miss the prayers. Your parents are not under your control, so you can only advise them. Get them authenticated speeches and warnings and talk to them over and over, but watch your tone and intensity so as to create desire and encouragement, not to create resentment and rejection.
By the way, I feel I need to be responsible to say that I checked the transcript of "Time to establish Prayer", and there were factual mistakes and errors regarding the rulings and opinions of scholars. The majority of scholars namely Hanbali, Imam Shafei, Malik, Ibn Taymeyya, are of the opinion that as per the hadith leaving prayer is clear kufr, and a muslim is no longer a muslim if he neglects prayer, but the apostasy law is not applied because there is no outright declaration and repentance is always hoped, and historically no muslim who neglects prayer was ever killed. The minority view, mainly Hanafi and modern Shafei math-hab and other scholars, see that it is not kufr akbar, but kufr asghar (minor) which is Kufr Bel-Neema, and there is no punishment to be applied at all by the judge or whatever. This 6 month jail sentence is innovated and no record of it being called for by the prophet or companions. There are other factual misinformation but minor ones, that was the major one. In general I would suggest using a different source for your family.