I don't think you could have killed her going 10mph or whatever from a yield. You'll be fine, the family is just freaked out because car accidents can kill people so they obviously want you safe. Just try to remember in the future, it doesn't matter if you miss a turn or have to take a longer route, it's fine. Being a few minutes late isn't the end of the world, this is just an early (and relatively non-life changing) lesson. Try to keep calm in the future and just decide how to re-route if something changes, don't worry about the few minutes lost.