There is a lot of diffrence between knowing/ speaking good english and teaching english comprehension. I was not satisfied with the tutor so I took tips from my mother (a language teacher but not in english).
Teach your DC to read fast once then read slowly in detail. Go through the answers and discuss why you think you got them wrong. We both did the bond comprehensions independently and discussed why we chose the answers we did.
Quiet agree with modernista. Depends on case by case basis. You can master it yourself if you have the patience, knowledge and understanding of key things to look out for. However, if the parents are themselves confused...it makes the child less confident then. All what you need is a good eye to skim/scan, good vocabulary, courage to read 2 pages of complex passages and ability to narrow down the option (which are usually very close to each other). Try the ones yourself in First Past The Post and you will see what I mean.