How to avoid a friendship drama over something very petty?

[CeCecilia]

I've unintentionally upset a friend. Someone I see daily.
The friend is not speaking to me or acknowledging my presence at all, which seems very juvenile, but I know this is her issue. I have tried speaking to her and being pleasant but just get ignored.
I really don't want to get into any form of confrontation, I know why she has decided to take this stance with me and it is extremely petty... I was meeting the needs of my child and so couldn't meet her needs at the time. The friend is very needy.
I feel silly being friendly and endeavouring to make conversation with someone who is blatantly ignoring me over something so ridiculous and I'm angry that she clearly hasn't considered that I needed to be with my child at that precise moment.
I don't want to fall out, I just want to be able to enjoy my day without drama and discomfort.
How do I proceed now without making myself look silly and without creating a drama over it?

More detail needed really. You could obscure some stuff for anonymity but it’s hard to tell by what you’ve written.

Perhaps it was not ridiculous to her?

Is it something you need to apologise over? Doesn't sound like it, but is it possible she doesn't know that? If she does know and is just being arsey, then to be honest, I probably wouldn't bother trying to repair things: I'd consider I'd had a lucky escape from a difficult person.

If you're kinder than me, you could write a note and hand it to her/put it through her door explaining the situation you were in and just saying that you don't want this relatively minor thing to cause unnecessary drama for either of you. "Can we just put it behind us?" But, ultimately, if she's the one causing the drama, it may be because she's enjoying it.

It may be petty to you, but is it petty to her?