If he has runny poop, you really need to get some fluids in him. Even a vet that doesn't specialize in rabbits can give fluids under the skin (Forgot what it's called). This is an effective way to make sure the rabbit stays hydrated. I think for me it was around $30-40?Although like Pipp said, he really needs to see a vet, rabbits can go downhill very quickly.
For now if you cannot get him to a vet, try seeing if he'll lick some water off a piece of hay. I've said this before, Pepsi loves damp hay and will nibble it down until it's gone. Do you have a syringe (without a needle) at home? Maybe 5cc or bigger? Yuo could try dribbling some water into his mouth (I find it hard to syringe with really fine liquid without splattering and maybe causing the rabbit to aspirate (inhale) the water, so I try to gentley push down and almost dribble it into their mouth). You can tell if he's hydrated or dehydrated by gently pulling the skin along his spine and letting go. If it pings back like an elastic band, he's well hydrated. If it goes slowly to return to it's normal position consider this a sign that he needs fluids immediatly.
Keep trying to convince your mom, you're doing a great job!