You apply for both at the same time because they are linked and the court is entitled to know that this is about more than just the forth coming holiday.
You DO NOT mention the counselling - that is something to work with the GP or school on
Under the Urgent application you inform them of the date of the holiday and the fact that she has threatened to withdraw her agreement.
I would suggest that your partner emails her tonight confirming that there are two bedrooms at the holiday home and saying that unless you have had confirmation by 10am tomorrow then you will be issuing an applictaion at Court with a view to a hearing date on Wednesday.
No discussion on the stupidity of the allegations - a simple statement and question
Assuming she does not reply then you take a copy of the email -NOTHING else (unless she texts a response)
At 4a you put
a specific issue order allowing you to take the child away from xxxc to xxx "
at 4b you say - she has threatened to refuse to allow the holiday and has refused to confirm via a reply to the attached email
And go for three days - still doable.