See, I think that is more reflective of the sin of impatience on the part of others than any sin of tardiness in you. You know the story of the tortoise and the hare? In modern life, we celebrate the hare and we denigrate the tortoise. Yet who really wins the race in the end? It is the tortoise, whose plodding pace and perseverance enabled him to repeatedly overtake the hare, even unto the end of the race! If you are a tortoise, and attempt to make yourself into a hare, of course you will injure yourself and have accidents! But if you accept yourself for who you are, and continue to plug away at life, and ignore or offer up the humiliations (the hare tried to humiliate the tortoise, too), then at the end of YOUR race, you will have won. People who do not struggle with timeliness do not understand those who do. They mistakenly believe it is a sign of disrespect or rudeness. Perhaps in some people, it may be. However, in others, it is not those things at all. I think a spiritual director or even just a few meetings with your pastor would be able to help you answer this question far better than a priest in the confessional (again, being aware that even priests are human and can be unable to understand every single human weakness).
I can understand this because I have struggled with timeliness to varying degrees at various points of my life. Sometimes, I run later than others. My husband is a fast, efficient worker, but he misses the details. My slowness enables me to notice those details and attend to them. With every weakness there is an attendant strength. I think, rather than attempting to obliterate your weakness, focus on working around it and on building up your attendant strength.
For example, getting everyone to Mass on time is real challenge to me. We do often run a tad late. One of the ways I have worked around the weakness is to lower my expectations of how “presentable” we must be before we leave. We focus upon clean body and clean clothes, and leave the dressing up for other people. Another way I have worked around it is to find the Mass time that is the easiest to arrive on time. Then we just do our best and if we run late, we can be reasonably sure it is not a sinful lapse, but merely an unfortunate event, because we tried really hard. What we will not do is run around getting ready, nor will we speed on the way in the car. Our family saying, whenever we go anywhere, is “And off we go, like a herd of turtles!!”
So I think I really understand your dilemma. And I have been chastised for lateness or similar offenses a couple of times in my work life (I stay at home now). I simply apologized, and told them they were right to correct me and thanks for the reminder. I informed them that I was not intentionally being late and that I would try extra hard from then on to be early instead. But, I am thankful that I am able to stay home now. A relaxed daily schedule is much less stressful for this turtle.