with most teenagers I'd assume "working" meant hanging out with friends but this sounds more organised. I'd let her try, if it gets too much for her deal with it then. Teenagers need to make mistakes sometimes and she will be on a train for hours so getting some rest then.
Is there any scope for you to agree a 'trial period' for a set amount of time, after which you review whether or not (based on any negative changes in her behaviour/general demeanor/tiredness) to allow her to continue?
There is also a chance of course that the idea of doing 2 extra days may appeal much more to her than the reality when put into practice?
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
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?"
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.