I'm glad things went better on the Tuesday.
Hope the talk goes well this weekend. I do still think you need to have it, perhaps prepare what you want to say in advance, just something brief you can keep repeating that will counter whatever reasons she may give you for needing to drop her son off earlier.
Work out what her reasons might be and think of something to say that will counter them all. Just go for one sentence, perhaps "I appreciate that bringing DN earlier means you have more time, but it means I have less and it's too disruptive for all of us."
That would work for most of the arguments she might put forward, from it "only" being ten or fifteen minutes earlier to her having a lot of work to do when she arrives to the traffic on the way to work and the parking situation once she arrives.
So if she says: "But it's only ten minutes and it makes such a difference to me/my day."
You say: "I appreciate that bringing DH early means you have more time, but those ten minutes also make such a difference to us and they delay me in getting my sons ready to leave."
"But I have to leave at that time because of the traffic. Leaving later means traffic jams and it's difficult to park so I'm late."
"I appreciate that but as I said, those ten minutes also mean the difference between us being organised and ready or us running late and forgetting things and it's just too stressful for me."
"But I have such a lot of work to do when I arrive, I need to get there early."
"I appreciate that, but I have a lot to do myself in the morning and I need that time to get my sons ready. I'm more than happy to take DN with us but we have to stick to the time we agreed."
All those arguments are are reasons why her time is more important than yours and so all you have to do is to keep reminding her that it is not. You have an agreement that she has broken to suit herself and although you sympathise with it you can't do any more to help her out than you are already doing.
FWIW, I'm not totally unsympathetic to her. If I left for work just five minutes late for whatever reason it didn't just mean I arrived five minutes late too. It would add an extra 20 minutes to my time in the car because the traffic had picked up by then, it meant finding a parking space in a busy car park rather than having my pick of it while it was almost empty and it meant arriving at work just on time with no chance to make a coffee, check my emails and messages or plan my work for the day before our daily meeting started at 8:30am.
But I think (and this may be the first time I've said this MN phrase) she sounds as though she feels she is more entitled to those extra minutes than you are and has given no thought to how disruptive it might be for you, your boys and her own son.