You need to apologise. And avoid accusing her of overreacting, or having no sense of humour, or minimising it with “but it was just a joke”.
If you can’t bring yourself to phone her, then email your apology. And btw, not phoning her because “she always phones me” is a rubbish excuse for not contacting her under these circumstances.
I’m also wondering how often you make these kind of “jokes”.
I used to have a toxic friend who would say all sorts of mean and nasty things to me as a “joke”. If I complained, then the standard response would be something like “but it was only a joke! You’re overreacting, you have no sense of humour, I can’t believe you’re suggesting I was being mean to you, you need to apologise to me for not liking my really funny joke” etc etc.
And honestly, there’s only so much of that sort of thing someone can take before you get to that one last “joke” that turns into the straw that broke the camels back.
I’ve no idea whether your “joke” is typical behaviour for you, but if you are in the habit of making bad “jokes” that are basically about your DD’s faults or how she’s not your favourite child, then you need to cut it out, or this scenario’s going to happen all over again at some point.