Yes I realise how self-employment works, but it's not something either you or she get to choose. Whether a person is defined (by HMRC or by an employment tribunal) as self-employed or employed depends on the nature of their relationship with the 'employer'. You will have a different relationship with the nanny who looks after your children week in week out than you would with a lawyer who gives you advice every so often or a cleaning firm who employ a cleaner on your behalf and invoice you.
Most nannies would not be able to be legitimately self-employed unless they are doing lots of short-term contracts, like maternity nannies do, or unless their hours vary weekly and they have lots of clients or similar.
It's up to you to satisfy yourself as to the nature of the relationship and make yourself aware of your obligations and her rights. Just because she invoices you and pays her own tax doesn't mean she is not technically 'employed' and therefore entitled to paid holiday, protection against unfair dismissal, maternity rights etc
If she were genuinely self-employed you wouldn't need anything in the contract about what she can or can't do in holiday time, you would just need something stating that x amount of notice will be given if services are not required. But if she will be working for you 30 hours a week all year except for a few weeks holiday time, she sounds employed and the document should be an employment contract regardless of how she gets paid.
Have a look here and here. If she can't send someone else to do the work instead of her, if she works on your premises, if she doesn't have lots of clients, is under your control and direction and gets a regular 'salary', then she will be employed.