I'm very sorry that you couldn't convince your mum that the kitten is better off keeping her claws.
However, I have to say that especially in young kittens with a competent vet (that's the most important factor!), most likely she will be fine physically. The odds are definitely in your favor. When you do get her back, please ask about pain management meds. Some vets won't give these as a matter of course, but it is important since she will be very uncomfortable.
Keep a close eye on her in the first few days to make sure she is eating and drinking and using the litterbox. I would confine her to one room so you can make sure of these things. Kittens can get dehydrated very quickly, and if there is any sign of infection the dehydration will be worse (and she won't want to come out to drink).
For now, replace the litter with newspaper as that will be easier on her feet. This is important because the granules of clay litter can get into her bandages and incisions and become infected. A bad experience like that can be one of the causes of litterbox aversion after a declaw.
If you have any questions about it, let us know. Sometimes we can't control the situation. Some of us have been through this, too. I got my kitten (Trent) declawed on the advice of the vet
before I knew better. His toes got infected, and it took a lot of TLC and a trip to the emergency vet at midnight to get him through it. But we did get through it, and he (so far) doesn't have any physical or behavioral problems (he's now 6 years old).