Yeah, my aunt tried to tell me her toddler daughter knew how to be gentle with animals. Then during an instance of forced babysitting, I heard one of my cats howling. I found out my little cousin was carrying the poor cat around by the skin on her back. Gentle, my fat ass. Needless to say, the cats got confined to the basement when Cousin came to rampage...and usually a lot of crying ensued because she wanted to play with the kitties. I hated imprisoning them like that in their own home, but if I didn't, they'd get lugged around by their skin or their ears or what-not and I didn't want to deal with the fall-out from family if I had to kill the kid. And then my aunt bought the kid a kitten soon after because she just luuuuuvvved kitties and just haaaaaad to have one of her own. I have no idea if said kitten/cat is still alive or not.
On one hand, I kind of would like to see the cat in the OP to get re-homed. Chances are very highly likely the kid is not being gentle with the cat, and a cat at that age does not need pain or stress in its life from a brat. I also would really not want the cat to get de-clawed (at 14 years old, I think there may be a chance it does not wake up from the anesthesia), nor would I want the poor cat to get put down if one day it smacks Junior in the face and snags the kid's eye. Fuck, I'm shocked Moomie hasn't put the cat down for scratching Snookums already.
BUT, on the other hand, like someone else had already said, being re-homed would freak the cat out too. Young cats take a long time to re-adjust to new surroundings...how would an older cat respond? And older cat aren't all that desirable in terms of adoption, sadly, so if the cat got left at a shelter, it's almost a guarantee that the cat would rot in the shelter and then get put down anyway due to lack of space.
I think the best this idiot can do is keep the cat and the kid separated as much as possible, since she most likely would be too busy doing TMIJITW to teach her kid to not manhandle the cat.