I wish your mother health, she will definitely recover. You are a good child, your mother is definitely proud of you. Regarding long-distance relationships – they make sense when both partners agree to this, and when they know the time of the final relationship at a distance and the date of your meeting. Based on your own words, now it will only prevent you from focusing on caring for your mother and at work, and your partner, knowing about your situation, is not ready to compromise. He seems to be trying to keep you as a fallback. I don’t think you need it.
Good luck!