Not sure if I should give time before I leave to care for sick family

I don't want to work anymore because the illness in the family is a serious matter (may pass away). I already knew about this since last month. However, I have been scheduled to work the next two weeks. They asked when is the last day I can work and I said I would prefer only one more week but can work up to the last scheduled day since that has already been scheduled, which would be another week. I didn't really know how to approach a matter like this. I feel like maybe I've waited too long and already starting to have some misgivings. I'm also missing the time I could be there at the hospital with them throughout the entire process.

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