yes the OP is entitled to unpaid time off for emergencies like this, but her employer allowing her to just ring up and say she's taking annual leave instead means she is not forced to use that right and is being given an option to take paid leave instead.
Unfortunately for her employer, allowing her to do this has had the result that she takes twice as much time off as she otherwise would, because her husband's employer is not so generous. So it's backfiring a bit and therefore understandable that the boss is a bit peeved.
Saffy85 why the
face? You are entitled to emergency time off, which would normally be a day or two. It's not to take off the whole duration of a child's illness, it's for things like taking a day or two to sort out alternative arrangements. So your boss commenting that it wouldn't be acceptable for you to suddenly take more than a week off isn't out of place, although it doesn't seem hugely sympathetic.
In terms of disciplinaries for sickness absence, yes perfectly legal and common to have triggers of how many sick days you can have before a disciplinary happens. Your sick days and the emergency (presumably unpaid) leave you might take when your DD is not well are entirely separate though.
Many employers are more generous, and will allow a couple of days extra paid leave, or time off in lieu, or will allow people to take the whole duration of a child's illness using annual leave, but it's by no means legally required.