I'm not sure there is an easy answer to your question.
Although being firm about your needs is difficult, what are you willing to do to not drive with her? Can you use S.E.T. with her to address the drive together?
What would happen if you changed the pattern when she threatens suicide and stated, "I am scared that you are threatening suicide, and I am going to call 911 for a well check if you continue to threaten suicide"?
If you say, "I know you want to drive together, but that doesn't work for me this time. I am going to go by myself," and she doesn't like it . . . she doesn't like it, but it is still okay to state your needs. Is it okay to put your needs first rather than worrying about making your sister happy?
This might be a different and scary way of thinking, especially when your sister is likely to react negatively. It is unlikely that you can tell your sister that you don't want to drive together AND she will respond positively. However, is there something we can do to help support you that it's okay to do something that makes YOU happier even if it means that your sister isn't? Your comfort and happiness matter.

One of the things my T has worked on with me is that doing what is healthier and better for me does not always "feel" good, but I would rather do what is better for me and feel uncomfortable than to do what is NOT good for me--meet the needs of dh's mom and family--and feel awful.

Pilate