Thanks to everyone who has posted, I've found this thread really interesting for the different perspectives it has given, and really heartening in terms of the couples such as IntheShed, who recognise that importance of a job isn't just determined by its salary.
As quite a few people have raised the question of my posting this in this level of detail, I thought I'd answer. I obscured some details in the OP and later posts because a) I didn't want it too recognisable and b) I was more interested in the general discussion than on the specifics of our business. In practical terms, this is my decision to make. There could be ramnifications from posting this, but that is my call. I am a partner in this business, and my "manager" is my co-partner, our HR adviser someone external. We are a fledging business and have been going for under a year. The deadlines which will be jeopardised if I were to grant this woman her request in full are our first for a client who will hopefully bring lots more work our way.
On the ethical side as to whether I should have posted this, yes I can see that there are arguments as to why I shouldn't. However, I have found this very useful in opening my eyes to different perspectives and arguments so I stand by it.
We pay this woman a very handsome salary - not megabucks by South East terms, but as much as she could get in any other organisation. In setting her salary, we didn't take into account whether she was the lower earner, or could afford emergency childcare etc because that was her decision to make.
This is not the first time she has made an emergency request (although none of the others have been so extreme) and to be honest, I am coming to the end of my tether with it. If she were a single mother, I would probably be more patient with it, but I do find it annoying that she expects us to respect the unequal domestic responsibility arrangement which she and her husband have agreed.
I gave her two options for the rest of August. One was that she brings her kids in every day, we put them in my office and I work in the main bit. The other was that she has today off (paid) to organise care for them and then gives me a call to discuss how she will do her work around that plan - bringing them in a bit/taking work home/leaving early and making up the hours in the evenings, whatever. I feel that both of these options are extremely fair. I was rather annoyed when in response to the kids coming in she said they'll "get bored". I'm sure they will, but that can be managed with books and DVDs and it isn't my concern.
If she decides not to come in for the next two weeks, well we are royally stuffed for an important client. In terms of managing her, that would be a serious disciplinary matter and I'm fairly sure it would be considered gross misconduct. If she provides a doctor's note, well I'll need to take some advice on that.