Is a son obliged to obey his mother by allowing his sisters to use the Internet, given his fears for them, or should he refuse?

The internet is a double-edged sword. If your sisters use it for permissible things, you have no right to prevent them, and the device should be placed in a visible location. However, if you strongly believe they are using it for forbidden things, then you are obliged to prevent them from using it, based on the Almighty's saying: (O YOU WHO HAVE BELIEVED, PROTECT YOURSELVES AND YOUR FAMILIES FROM A FIRE). You should inform your mother, and if she continues to allow it, then you must prevent them yourself; for there is no obedience to a creature in disobedience to the Creator. This should be done through advice, guidance, and good admonition. You are obligated to obey your mother if she tells you to allow them internet access, unless it involves committing something forbidden.