What is the ruling of Islamic law regarding a daughter's intervention to advise her sisters to adhere to the hijab and perform prayers on time, if this causes family problems and the mother objects to this intervention?

Enjoining good and forbidding evil is an obligation upon a Muslim according to their capacity. It is your duty to enjoin good upon your sisters and forbid evil from them with wisdom. Your mother is not permitted to prevent you from doing so; rather, it is her duty to do it herself. Explain this to your mother gently and politely, while still honoring her and being kind to her. If you fulfill your duty, their non-compliance will not harm you, for Allah Almighty says: "O you who have believed, upon you is [the responsibility for] yourselves. Those who have gone astray will not harm you when you have been guided. To Allah is your return all together; then He will inform you of what you used to do." We advise you to continue counseling them gently and wisely, encouraging them to associate with righteous women, seeking help from some righteous relatives to advise them, and persistently supplicating for their guidance.