Oh I have sooooo BTDT with DD1.

In the end I *did* get it cut. I took her to a really good hairdresser (mine) and had her give her a nice, manageable style cut. It looked really good. Also discussed with the hairdresser the "deal" - namely - if she cares for it, she can grow it longer. Hairdresser (not me, I'm standing calmly on the sidelines) explains what is needed, how to put it up, how often to wash, how to comb. Suddenly - now it's no longer a power struggle with mummy dearest - DD1 starts to care for hair. Each time we go back to the hairdresser, decision is reviewed. DD1 now knows - do it right or it'll be chopchop time again. End of issue.
This is exactly what I did with my DD and she loves her hair! It's so much easier for her to look after now and she now tells the hairdresser what she wants when she has it cut.

Knot free hair is bliss!