I'm inferring that the patient portal your doctor uses is not MyChart. (Please let me know otherwise.)
Check your spam/junk email folder. The activation or authorization code may have been sent there. (Apologies if you've tried this already.) If you find it but it doesn't work, that may be because it has a limited duration, for security's sake.
The next time you contact the hospital, ask for the Patient Ombudsman. The role may be named something else, but this office (often part of Patient Services) is specifically tasked with helping to resolve patient difficulties. In general, they are also the first place to go when a patient has a serious complaint about a medical provider; this helps ensure that patient care doesn't suffer. You may be able to find the Patient Ombudsman phone number in the hospital website, because it's often a required role for hospital accreditation.
When you do get access to the app, check to see whether you can grant one-time access to your test results to your sister. (That is possible on the similar app my health system uses - exporting a single test result, as a PDF.) You should also be able to grant broader access to your sister, but the fact that you wrote "hounding" implied that you might want to hold off until you know what exactly that means in this context.
Hope this helps - good luck!