Discharged patient before oxygen test

You would have a case if there is medical reason to think (i.e. the opinions of other doctors, or evidence of standard medical practice) that it was careless to not do the tests or get oxygen. It's not enough that you asked for it: you are (we presume) not a doctor, and your opinion or requests do not bind doctors or hospitals, which are instead obligated to do what they think medical appropriate. So if what they did was not up to current medical standards--it went against, for example, "textbook" advice for this situation, and/or other doctors would have done things differently--then it may be malpractice; but if other doctors or the medical profession would regard what was done as reasonable, then even if there was a bad outcome for your mother, there would not be liability. Liability is only imposed when the doctor/hospital did something wrong, not just becasue things did not work out well.
Note that there is generally no compensation for stress or "toll" on family members or caregivers; generally, even if there was malpractice, there is compensation only for the additional medical or care monetary costs incurred due to the malpractice, or for "pain and suffering" for long lasting significant life impairment (i.e. impairment beyond what your mother was already experiencing giving age and any health conditions) lasting (typically) months or more. And at the same time, malpractice suits can be very expensive, since you would have to hire an attorney (unless your mother is prepared to be her own lawyer, since it is her malpractice case, which is NOT recommended) and also hire a medical expert (doctor) to write a report and testify. While you may wish to speak with a malpractice attorney about this (many provide a free initial consultation to evaluate a case; you can confirm this before making an appointment), it may not be economically worthwhile to bring a case in this instance.