if a nanny is working for you solely and you're dictating the hours, you are an employer.
Yes, HMRC would look at the facts of the situation, such as who has control. In a permanent 4 day a week job, it will be very clear that the relationship is that of master:servant - so employer:employee. You call the shots, so they are your employee.
Ignore what any friends might do. You are the one that get's in trouble if you get it wrong, so register as an employer and do PAYE regardless of what friends do or what the nanny wants you to do. You want the relationship to be that of Employer:Employee, you don't want your nanny turning round to you and saying they are not able to do x day, y day.
Every 4 - 6 weeks, we would need 5 days, 7:45am - 6pm. How are these extra hours normally paid? Can online payroll companies cope with this? Or do you contract to pay the 'standard' hours monthly and then top up with an additional payment or cash?
Payroll companies should be able to cope with some overtime being added onto the following month's payroll. Talk to payroll companies you are considering using about how much notice they require for varying the number of hours worked in the pay period.
Contract wise you could contract for a set number of hours per year, with a suitable annual salary. You will need to discuss with applicants with regard to this 5th day, as it will not be suitable for candidates who do other work. Talk to them about how much notice they would get of these extra days and that working that day is not optional, they must do it.
For holiday entitlement, work out the total number of hours worked per year and use that to calculate holiday.
Why 7:45am? Could you make it more attractive by having that start time, or a bit earlier if needed but paying it from 7am? So you have whole hours, which makes pay a little easier as you are giving the payroll company a whole hours figure and holiday entitlement a little easier. You can do it as .25 of an hour but you want your nanny to do this additional day, you don't want them getting other work on the 5th day each week, you don't really want to pay an overtime rate for it, such as time and a half. So bump salary a little, rather than high overtime rate. Keep nanny happy whilst keeping your cost down.
With two children under 3, I 'think' it works out about the same cost as full time nursery.
I would say it generally costs a bit more than nursery (in my area nurseries are around £55 per day, per child) but it comes with advantages, such as not having to get your children up in the early hours of the morning.
However, what other costs haven't I factored in? Salary (duh), mileage reimbursements, kitty of £15/week, extra food £10/week, cost of 2 weeks extra childcare when nanny goes on holiday of her choosing, Ofstead registry £103/year, Public Liability Insurance £80/year.... What else am I misssing?
Employers National Insurance, Payroll Admin (these costs may have been covered in your other points)
Kitty - £15 a week may be a little low but is certainly something to start with. It will depend on area and cost of the activities they do. Keep in mind that as children get older they tend to cost more, as lose things like free travel, free admission, low cost admission.
Nanny would have more holiday than 2 weeks - I guess you are covering the rest yourselves so are not counting that as being a cost.
Your Employer Liability insurance may be part of your Home Contents cover, check your policy. You would not be paying for the nannies Public Liability Insurance, that is something they need to pay.
Nannies birthday present
Nannies xmas present / bonus