I don't know, I have sympathy for the OP and also for all the mums who have children at an exuberant / difficult age.
All children go through phases of testing their carers limits and 'look for trouble' to see what will happen, IYKWIM.
I do think the OP has a problem with her friend. it seems to me that the Op wants her friend to lay some boundaries for her DD, and that by saying yes dear yes dear isn't having any effect (and it isn't).
FWIW I had a SIL (now X-SIL) who just kept saying 'oh don't do that' 1000x a day to her DD, and she would never follow through on any disciplining consequences, and her DD used to ramp up that bad behaviour to get attention. So I do understand how upsetting it can be if it seems that the child has no boundaries or discipline being set for her.
For me, I didn't expect very much from my DD when she was that age, but I would expect her to use her inside voice when inside and to share and be nice when we were with others.
If she was screeching, we used to leave. EVERY TIME. And soon DD learned that screeching was not acceptable. She didn't do it much - just to see what would happen as an experiment. So I was very consistent with the consequences.
BTW if we were going somewhere that was restrictive socially, like a visit or a restaurant, we used to go first to the playground / park and let off steam - fair's fair after all. hth