Absolutely take the job.
Your SC's years of compulsory education end at 18.
If she wants to continue her education beyond that point, then she needs to do what every other 18 year old up and down the country does, and make a choice of where to go and what to study based on her circumstances at the time. She cannot expect or ask the rest of her family to shape their lives around her non-compulsory educational choices.
If she wants to stay on at her FE college for the foundation year, she needs to either find accommodation or be prepared to commute. An hour each way to college is not that bad - many school children in rural areas do more than that every day from the age of 11 - so if she wants to stay living with you, she's got that option. If she doesn't want to stay living with you, then she'll need to find accommodation where you currently are and apply for a student loan to pay for it.
Teenagers are incredibly selfish and they do expect the world of every adult in their lives to revolve around them far beyond the point where they can reasonably ask this of their parents. They struggle to see their parents as people with their own hopes, dreams and ambitions, and think they exist purely to serve their needs. (I'm a secondary school teacher, so I know of what I speak!)
I would, if I were you, gently and kindly and calmly explain to her that this is a dream opportunity for you, that you have waited a long time to be able to go for an opportunity like this because you have prioritised her and her siblings while they were in compulsory education, and you really want to be able to move forward with your career now all the children have grown up and will be moving on with their lives. Promise help and support to make whatever plan work and a bedroom in the new home, but make it clear that you will not be able to commit to staying where you are while she carries on her education past the age of 18.
She will then have plenty of time to get used to the idea and make a plan. As others have said, teenagers are so changeable anyway - this is what she wants right now, but who knows what that will look like in six months or a year. Do not build your life around a fickle teenager's plans!
I would also reiterate what others have said - I wouldn't have any more discussion anyway until the job offer is on the table. I'm sure we've all been in situations where we've been promised things and been a shoo-in for a promotion and not got it. So don't count your chickens before they've hatched.