Lots of good replies here.
Yes, taking the power away and co-opting the use/phrase/joke will neutralize the impact.
On the other hand, kids do need to learn how to feel expresive of their feelings, so neutralizing one will not help unless you replace with another.
So your DD has found your button. Your issue then?
I had "I hate you" for no particular reason.
Maybe they were whetting their toungs rather than trying to hurt me. I think this is more to do with personal empowerment than inflicting pain. Anyway, I did not like it, but responded with a bored "yeah yeah, I'm so horrid. So which juice/cookie/toy do you want? Is is raining, what's for dinner? Oh look, the cat pooed in the flowerpot!" and got on with life as per usual.
But empowerment is important, so the much more benign "You are a silly Daddy" generated a feigned strong outrage and hand on hips and all manner of acting angry and offended retorts. Always this ended in romps and laughs.
They get what they want (response) and I don't get what I don't want.
"I hate you" was out the window by the end of the week if not earlier.
When the heat is off your SO can help you out here with a pre-planned "event". They can introduce a phrase (but best stick to one, otherwise it becomes an exercise in insults).
"jelly belly", "silly billy", "puffy mummy"... whatever it is, this is all a game, and SO should resolve it soon, with hugs.
Kids do need to feel in control, even if it is only a little. A model positive response gets better results all round, and saves you from opening your own wounds.