Shelia not having the boys living with her doesnt mean Shelia wasnt functional in the normal sense.
It was of course a much better idea and common sense for the boys to live with their father while she sorted out her problems she had.
It appears that Shelia often got into money difficulties which gives the impression that the bank of Nevill and June were not just shelling out for everything ( although they more than likely got her out of debt)
The debt can show it may have been reckless spending by shelia or she just couldn't support her lifestyle on her wages.
I agree with most of what you say regarding Sheila's functionality, or lack of. I do, however, think well paid occupation, for her, in the working world, was very limited to non existent. She was trained for nothing. Everything she tried, failed, ergo, she either had to have been on benefits, or collecting from the bank of N&J. The tiny amount of 'cash in hand' she'd have received for cleaning or waitressing, probably wouldn't have kept her for a week. If her flat was leasehold, the maintenance charges would have been astronomical. She'd have needed to clean or wait from dawn to dusk to fund it. I imagine she was a huge drain on the Bambers' finances.
I'm not certain that she'd ever aspired to anything remotely academic. She appeared to have gone for employment which looked glamorous without any input of effort. Neither modelling nor hairdressing/manicuring fit that description! -I can speak from personal experience. I never earned well until I was teaching, but such required much hard work, and qualifications Sheila didn't have- and as she appeared to like to wear her nails long, typing would have been out of the question!