Helen Clements and her children Charlie and George told ITV News that her car had "overheated", causing the family to abandon the vehicle at a lion enclosure at Longleat Safari Park.
Ms Clements said: "What we thought we better do is, because what you are supposed to do is sound your horn, so we did. But my son George thought he better get out the car, so he opened the door, and got out the car. And I just said "George don't get out of the car"".
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The 41-year-old father of six died last Thursday - a week before he and the band had been due to begin touring in North America.