What's difficult to give advice o. Without seeing all your relevant paperwork is the definition of gross misconduct in your case - there is not really one standard definition, it's set by the terms of your contract, handbook (although you probably don't have one) etc
One interesting reason for dismissal that does not have to be either redundancy or dismissal is for 'some other substantial reason'
The SOSR dismissal is for things that don't really fall user one of the other headings, but are significant enough to warrant that course of action
Now, I would argue that a completely intransigent employee, who is expressly going against the stated terms of her employment and the express decision you have already explained to her, is reducing the relationship to one that is no longer sustainable and you have list trust and confidence. So, potentially it could be a SOSR case.
The key thing an ET is looking at in reaching a decision re unfair dismissal is whether an employer has acted fairly ie made a reasonable decision that another reasonable person would also reach. This is clearly quite subjective, but I think if you go doe. He route of saying to her
"I have considered your request. In light of the difficulties caused to me in having to find an alternative solution if you do not attend work as contracted to do, I regret that I cannot agree to further leave. If you go ahead and take the leave anyway, I will be forced to consider that you no longer wish to see out the remainder of your contract"
BUT - and I hate to say this - you have already given her extra time off...so does another 2 days really make a difference? If you can genuinely say yes, I'd consider the SOSR route. If not...well, no good deed goes unpunished.
An employment lawyer friend of mine recently put the odds of winning a case (even if you really think it's a good one) at no more than 75%
So essentially you have to take a view on the risks
NB: I work in HR and used to employ a nanny. I have also uttered the words 'I am never employing another nanny'. It is not easy...