I suspect that the OP won't be coming back but just in case she does - even if she doesn't have any developmental delays, she may have ADHD. Her inability to plan ahead and foresee consequences could well be linked.
As to whether this is her fault or your DH's, well it's really a combination. Of course it's hers, because she IS old enough to know better - but on the other hand if her father knows full well that she frequently "forgets" or doesn't do the right thing, then he should have helped her out, not just let her burn.
I burnt several times as a teen in the UK (also redhead, pale skin) and it isn't at all pleasant. Worst was revising in the back garden for my O levels - I fell asleep, oops! - and the burn just kept developing after I went indoors. Mum gave me calamine lotion but it just dried the skin out (bad idea) and next day my whole chest/shoulder area was one massive blister, which burst when I rubbed it (it was itchy). Now THAT was fucking painful. But my own fault, of course.
However, there is no need to be sitting up with her unless you believe she actually has heatstroke, which I've also had and is truly horrible.
I also don't agree that, in the UK, she needs to be wearing sun screen daily. I live in Australia now and I don't wear it daily either, but I probably would have as a youngster. Vitamin D is made through sun exposure and we need to have some sun to make it - not too much so that we burn of course, but some.
However, for any length of time in the sun, sunscreen is imperative. She needs to learn this, and fast.