OP, you may think of your nanny as salaried but the truth is that she is legally an hourly worker and needs to be paid accordingly. She is to be paid for all time worked, and overtime for all of these chunks of time you are late.
Your cavalier attitude towards this, and your routine lateness, are absolutely worthy of a curt attitude, and frankly - unless you are paying $25/hr, you should be prepared for her to quit.
I am as respectful of our nanny's time as I want her to be of mine, or would want anyone else to be of me. Her day ends at 6 pm unless we have asked her previously to stay late for some reason, or something horrific happens to make my commute home a nightmare. I structure her hours and my day to ensure that I am home by 5:45 so I have time to change, see her for a minute, and allow her to leave on time without it being stressful. If I'm going to be late unexpectedly (which happens maybe 3 or 4 times a year) I let her know and am profusely apologetic. If I'm more than 5 or 10 minutes late without scheduling it in advance I would pay her - though this hasn't ever happened.
You are really in the wrong and you're giving the rest of us a bad name.