I thnk you should discuss it with her. Perhaps explain that you want to take the unpaid leave to give her your help and support and spend time with her now and ask if she could support you financially during this time. You wouldn't have to put a timeline on it but just talk about it being for now. I wonder if she might then feel good about being able to be involved in her care, as she will be helping you to help her.

Or, could your sister and aunt support you know and be repaid later?

Also, some funds like retirement, 401k's, etc have an options for loans and hardship withdrawals for life's unexpected events that you might be able to tap into.