What a kind and loving daughter you are!
What Mom says is true --- it is our nature to come into this world, live it as best we can, and then leave it to the next generation . . . but I do understand what you are saying . . .,
You want Mom to have a great life, but I think the way you contribute to that is looking at the situation a bit differently:
1. Your Mom is healthy and exercises. High blood pressure is not uncommon and is well managed . . .there are just as many stories of peoples parents living long and uneventful lives so don't focus just on the negative. We cannot control Nature but we can control our behaviour. So, make time to spend quality time with her. It does not have to be big things. If she goes to exercise classes, see if you can go with her. Invite her out for a girls' shopping trip even if you buy nothing.
2. You don't want to be left alone because right now your strongest emotional ties are with your Mom. Although this may not be something you might easily envision, but if parents do their jobs appropriately, then their children are never alone even once they have died. Your Mom is emotionally, psychologically, and physically linked to you.
3. From my perspective, the very best that you can do is to try to see things from your Mom's point of view: she does not want her 13 year old daughter to worry about something that no one can control. She wants you to grow into a happy, productive person. If the worrying is out of hand, ask her if you might be able to speak with a trained professional . . . not for meds, etc., but for some management techniques to help you to look at what you are worrying about and why . . .
Your Mom will have a great life when she sees her children as happy and leading productive lives and she too will live the life she wants as she takes care of those issues that are stopping her . . . but, just as you have to deal with your worrying, she has to deal with your dad's family and your dad . . . . so, both of you really need each other to manage your worries . . .
I know that this probably does not help you a great deal . . . but, dealing with these big ideas of life and death is a process and it takes time . . . ask questions but don't assume that anything you read or hear is the complete truth. . . . right now, the best that I can see is that you and your Mom spend some quality time together so both of you can enjoy each other's good times . . . .
Please check in when you can . . . even if it is a quick hello and let us know how you are doing . .. . take care, kc