Gosh they know when to play up dont they!
We use a reward/ punishment system and the 1,2,3 If you do this when we get home you can.... Im gonna count to 3 and if you dont do.... then you lose.... for today.
We also stop what we are doing- if you dont hold my hand we go home. And we do it. If you dont sit in the trolley we go home.
We have the naughty chair. Stop that or you sit on the naughty chair. I've been told to sit on the naughty chair for yelling too.
It all takes time for them to see that this behaviour = this from mummy/ daddy. And they resist wickedly at first but they soon get use to it and its almost comforting for them in a strange way.

I dont know if any of this will help. Your DD is at one of those ages where she wants to assert she is a person in her own right.
Hugs and sending patience vibes your way