No further discussion. You, on the other hand, were taught to be on time and feel very anxious when you run late. You've asked your mate repeatedly to respect your wishes. She says OK but continues to be late. First, assess if your mate is always late.
Some people are on time for certain events but give themselves more latitude for others.
If this is your mate, discuss what events you categorize as most important to be on time for and those where you would be willing to go along with your spouse's more laid-back time frame. Sometimes, too, one spouse will define lateness differently than another. I've seen discussions like this clear the air and give both spouses a better understanding of the way each of them views time. Take separate cars. It may not be ideal, but it will keep you from starting every event with a hostile attitude and feelings of helplessness.