Of course not. Crates are only meant for transport, recovering from illness, injury and/or following surgery Only when no one can supervise.
Unfortunately it's a family dog, Mom's house, her rules, so you have no say in the matter, as minors can't own property dogs are property. Deal with it, respect her decision whether you agree or not, She's the adult, you're the child, when you become an adult move out.
If the dog was already trained/housebroken it should be taken outside for walk/elimination times, minimally 3-4 times daily 30-40 minutes each time. No dog should be left alone for more than 3-4 hours without a chance to eliminate outside each day, let alone confine it to a crate, even if it was never housebroken, it would need to be taken outside for elimination every 1-2 hours, daily not kept in a crate.
In addition to the daily walk/elimination times already mentioned, all dogs also require daily aerobic exercise, such as running/swimming, minimally 20-30 minutes daily, anywhere from 1-4 times daily, and daily mental stimulation, such as obedience training, 10-15 minutes minimally daily, anywhere from 1-4 times daily depending on the individual dogs age, health, stamina and tolerance.
No dog or pup should be kept under these conditions regardless of breed, Type, and/or lack of breed. Doesn't matter if it was a poorly bred, genetically deficient, BYB/Puppy Mill dog/pup, and/or shelter/rescue/pound/Craig's list $200. "Shih Tzu Terrier", mix JMO. That does not excuse how it's being treated, but as already stated, unfortunately there is nothing you can do about it, being a minor child.