Legal Rights on Taking A 'snow day' - found this article, thought it may be an interesting read.
According to the legal person who wrote it, an employer could let an employee choose to take the day as Annual Leave, Unpaid Leave.
The first two times she failed to turn up to work, when she contacted you, you agreed with her that on that specific occasion that you would pay the day... so it's Paid Authorised Leave. Is that right?
Now you are saying that if it happens this week (you don't know as yet if she will fail to get to work) then you will not be considering it as Paid Authorised Leave... instead you will either permit it to be Unpaid Leave, or let her take Annual Leave. Is that right?
Not sure how you having problems in paying for alternative care is her problem... if she has Annual Leave available to be taken and IF you agree that it can be taken, then this months payroll will include the day as paid. If she is aware of your difficulties in being able to pay, then she may say she would take the day as Unpaid Leave.
Her financial situation isn't your problem, I feel you are entitled to say that it can't be taken as annual leave. I don't believe that you have to authorise all annual leave requests... so you could refuse to let her take the day as annual leave... but permit it to be Unpaid Leave.
I travel 8 miles to work (normally - my snow route is 15 miles via Motorways as those tend to be clear of snow), I'm a similar age and my boss has been lovely about giving me shorter days when it's been possible to do so. I've got to be at work at 7am tomorrow, setting my alarm for 5am. I am intending to make every effort to be at work on time, as my boss needs me to take over at 7am. I have no issue with that... what actually happens tomorrow is what happens though, there are never any guarantees but my boss knows that I will make every effort - I hope the slush does not freeze! If I can't get in, then I would accept it as unpaid leave, or annual leave.