They messed up the children's ages.
Unless Wikipedia is wrong, (and it most certainly can be) Lucy is 9
Years older than Tim, not 6. Does anyone know if it's the film or Wikipedia that screwed this up?
Yes, Lucy is 9 years older than Tim (and 3 years younger than Robert). I don't know exactly why the filmmakers decided to compress the time frame, but they frequently do that in films.
BBC did a recent documentary on Hawking where they interviewed Tim (and Lucy -- Robert lives in Seattle). A funny part was when Tim tells the interviewer that he used to program swear words into Hawking's speech box!
http://metro.co.uk/2015/06/14/stephen-hawkings-son-used-to-put-swear-words-into-his-dads-speech-machine-5245405/