What sort of 'studying' will she be doing in London? Does it involve a long journey to get there?
To be honest if that was my teenage DD I would be inclined to let her try it - is there any 'penalty' involved if she has to give it up? Then she can make up her own mind if it is too much or not. I used to work seven days a week in my teens and early 20s - I loved it, didn't have a home/housework to worry about, had lots of friends where I was. Couldn't do it now !
Most parents struggle to get their teenagers out of bed before midday so the fact she wants to study must be a good sign surely?
DS2 (16) has been working in a part time job over the Summer. He recently did 7 days in a straight, hours varying 11-3, 12-6,8-3. He was knackered. He doesn't sleep brilliantly because of his asthma, his meal times were 'out'. By the time he got home, had something to eat, got changed, etc, there was no time for anything else. He was like a machine and it took it's toll.
I should imagine doing it permanently could make you ill.
Does she stand to lose anything if she starts it and drops one or two days? If not I would be inclined to let her try it - she'll soon find out why it's not a good idea and that's the point where you offer sympathy and suggestions to try and tip the balance a bit.
Because she needs to get a part time or baby sitting job on weekend in order to make herself more rounded as a person for cv or applications.Its a tough market any kind of work experience is worth it's weight in Gold.People will not neccesarily take seriously someone who has limited life experience especially in more people orientated professions.
Does she have anywhere to stay if she is doing 2 days? Otherwise her Sunday journey will be terrible, lots of engineering works, bus replacement etc, a 3.5h journey can easily become 5 hours, and that is far too much. How would she feel arriving 2 hours late for class and then spending hours on a bus instead of a train?
What is wrong with homework on the train? Lots of business people work on the train.
I think I find 'fun' things easier to say no to 'Can I go to a mixed sleepover' "NO" 'Can I go to a gig 100 miles away with a friend driving' "NO" 'Can I have a party while you go away for the night' "NO"
'Can I work even harder than I am now; to better enable me to have a career - even tho' it's a fairly stupid plan and may cause me real problems/issues' "Well I'm not really sure dear, do you think it's wise?"
I think you should let her try it tbh. I may be slightly biased in that I (and a lot of my friends) did not grow up in well off families and therefore had to work nights during the week plus weekends from 16years of age onwards (through sixth form at school and first degree at uni) in order to pay for the nice clothes/socialising/extras that are important for teenagers. To be honest yes we were tired at times but we all did fine at school/uni and are in professional jobs now so it didn't do us any harm and in fact probably contributed to the development of a good work ethic overall. Teenagers and young adults tend to have more stamina for this sort of thing and at least she would be participating in/studying something she has chosen/enjoys on those extra days not breaking her back stocking shelves for some asshole just so she can go to the cinema with her friends