Well. I bought a detangling brush, a Tresemme smoothing shampoo and a defrizz spray. I've also used a leave-in conditioner, during the wash instead of after.
And it seems to have helped a lot! We'll be having a hair wash within the next couple of days, so lets hope the improvement continues.
And for the poster who said she should do it herself - if I find it hard to manage, I don't see how the child could possibly do it. After she had chickenpox and spent three days on the sofa, it was so badly tangled right down to the roots that it took two hairdressers to get it all untangled. Urms I love your word - smushing. It's a perfect description of what happens.
As for cutting it - she has only made friends in school in the last year (before that she often cried because of having no friends) but her two new friends have lovely Indian silky very straight long hair and I think she longs to have hair like them. That's why she doesn't want it cut - I think in her mind having long hair makes her the same as them. That's 10-year old logic, I know.
So I reckon I've cracked the problem. Thanks for all your helpful posts and fingers crossed!