I don't think 50/50 is a good idea. I also don't think it's normal practice as I've never had that in any nanny job and also not in any non-nannying job. So to me it is Not Normal.
As the employer you can decide to approve or not approve all requests an employee makes for taking holiday. In a good working relationship with a nanny I feel that the employer tries to accommodate the nannies wishes as much as possible, whilst at the same time not making it such that nanny gets 100% choice.
Some nanny employers may well go on holiday more often than the nanny is legally entitled to take off as holiday. In that situation, the nanny could well be asked to do some duties at their place of work but many nanny employers I feel would give the nanny the extra time off.
The contract/written statement I feel is setting out the minimum holiday entitlement, not what may actually happen in reality. If you were going away for 6 weeks this coming year, you would not want to write 6 weeks holiday into the contract, as in the following year you may only go on 4 weeks holiday, or even none at all.
As a nanny, if my boss has approved all the holiday dates I have requested and then my boss decides they are going to take additional holiday, I would not be happy to take unpaid leave, as I've kept to my side of the deal which is that I would request holiday and they would approve or deny my taking that holiday.
So I don't feel it's on to ever in the position of not paying your nanny. Your nanny is signing up to a job which is all year round, not a job which is only at the times you decide you are not going on holiday. Ok I know you are not likely to decide to go off for a 3 month period, or take lots of weeks off here and there, but some people might. You agree to pay an Annual Gross Salary based on the working hours done and to include the holiday entitlement (at least statutory minimum of 5.6 weeks if they are a 5-day a week nanny). Nannies budget on getting their annual salary. If you were to then decide that some days were unpaid... then you would no longer be paying that annual salary... so I feel it would breach that part of the contract.
So I feel that if you decide to go on holiday more often than the nanny is entitled to do so, then you either give the nanny the time off as paid, or you ask them to come in and do some household duties (though finding enough of those to fill full days/weeks I feel may be quite hard).
You want to keep a nanny for many years... be nice to them... if you go away more often than the nanny is entitled to take off... give them the time off Paid.