Thanks for your extremely detailed reply - it was really appreciated.
I have managed to get on top of the nits - I used Delacet which is some sort of strong herbal concoction and I picked out what I could with a comb and coconut oil.
The Neem sounds interesting though, I might try that next time - if there is a next time. If there is a next time I think I will collect one or two nits and take them in the sauna with me, just to see if there is a temperature that knocks them out. Hopefully it will be an ok temperature for my children! I don't want them getting too hot! I could have done all this this time, but I didn't think it through, I just wanted rid asap.