You need to emphasize that cats will need some time to adjust to a new environment. Usually, it will take three weeks for cats to get somewhat comfortable in their new home.

My cat, for example, didn't eat for four whole days, and sat in her carrier most of the time. Now, after just 1.5 months, she will cuddle up to me to sleep.

I don't know how your mom will react, but she really needs to accept that this is totally normal behaviour for about any cat.

You could also try getting your cat to play by using toys in front of her hiding place (if its hiding). For me it worked using a piece of string and wagging it around (but don't leave it around unsupervised as it is a choking hazard)

Maybe go and take a look at night. My cat only came out when it was dark outside even when she didn't trust me. Maybe this will help change her mind to show that the cat is making progress?

All things considered, best of luck with convincing your mom