I would go directly to the director and express your concerns. Word them as concerns and not as complaints. Tell her about the traffic situation and apologize. Express concern that the center be flexible enough to allow for situations out of your control. Tell her it seems to be a problem that you can't pick up your son earlier and ask if she'd prefer that you find child care elsewhere. If she replies in an understanding way, wait and see if attitudes improve before removing your son.
My grandson was in an in home day care and tho the caretaker was warm and co-operative in most cases she came across somewhat cold if I was late picking him up. I apologized and she warmed up and said she has to be strict with the pick up time because she has moms who are chronically late and try to wiggle out of the late fee.
She did continue to be cool when I was close to closing time. It seemed like it was a defensive demeanor automatically put in place for everyone.
She continued to be friendly and allow exceptions when I called ahead of time.
You don't say how large the facility is but it sounds like it's large which makes it more difficult for the director to treat you as an individual instead of one of many, some of whom will take advantage of her if she's not tough.
I suggest that if you haven't spent time getting to know her on a more personal level that doing so might calm the waters, It's more difficult to treat a "friend" in a cool, imperious manner. And....most importantly, you'll have a better idea of how concerned she is about treating your son in a warm and nurturing way.