I mean, he challenged me to prove that my mother existed, without seeing her. Obviously I couldn't.

You could, if you have sufficient sharp ears. Or smell sense. The point is, if you accept current physical law, even if your mother is space-like separated from you, there'll come a time when your future cones will interact, and in that case, provided you have sufficient sharp instruments, you could prove her existence. You could even entangle your matter with her, thereby reaching non-locality (or creating another universe, if you prefer realism). The only way to physically separate yourself from your mother is to make her cross an event horizon (cosmological or otherwise): in that case, no more physical interaction can occur and she will be gone for good.

Otherwise, as others have noted, the only way left is solipsism.