@Infinite_Studios ‘Bursting into tears’ is a reaction to a story with a strong emotional core. Although the exact impact may vary across individuals, but it is humanity and relatability that hit us when we watch or play an emotional scene.

Coming to your idea, your elevator pitch (that's how I'd characterise the summary that you gave) does have the potential to become what you want it to, and I would encourage you to think about the hows and whys of the story. What happened to the mother that brought her so close to her end? How does the daughter know? It is quite natural for the daughter to want to save her mother's life, but if it endangers her life, it is also natural for the mother to want to save her daughter. That makes for some interesting conflict and also a few emotional scenes. The daughter may have to choose between living with the knowledge that she could change things (though at the cost of her life) or dying with the knowledge that her death will grieve her mother. Add to it the third option of the girl making the ultimate sacrifice in secret (e.g. after telling her mother she won't sacrifice herself) and you can bring out some interesting character traits.

You can introduce some grey areas and flaws as well. Make the girl a proverbial ‘good-for-nothing’ or make her somehow responsible for her mother's condition (or, at the very least, make her feel responsible), which may be easier to pull off in a fantasy genre. That way, her motivation can be more than just a daughter's love for her mother - a quest for redemption.

How do you achieve it? I'll analyse one of the most heart-wrenching moments from animation. Excuse the example from outside gaming, but I'm sure we know Bing Bong from Pixar's Inside Out. Why could he make us cry? He isn't even supposed to be real. Most of us probably saw things his way - someone who lies forgotten but does everything he can to save those he cares for, even though they may no longer even remember him. In a remarkably short span of time, that bond was built through flashbacks. We get a bit of foreshadowing when his vehicle (I forget what it's called) fails to make it because it's too heavy with two riders, and also when his hand begins to fade away. He says he's ‘got a feeling’ this time (that they're going to succeed), and we knew what was on his mind. His last scene has him embrace his fate of being forgotten (arguably worse than death) with hopes of seeing the unfulfilled dream he cherished become Riley's reality one day. We probably cried because we saw things from his eyes, and we saw in him someone we've all wished we had at some point.