Assuming you are not in London, 10 gross per hour sounds about right for a qualified experienced nanny.
8am-6pm Mon-Fri won't be an issue - actually quite nice hours. So £100 gross per day, £500 gross per week, £26,000 gross per year. Employers NI around £2600 per year.
It does not affect the National Insurance you pay on your income. However your work may offer you Childcare Vouchers which can affect what you pay in YOUR income taxes, perhaps your inlaws are getting confused by that.
A nanny working 50 hours a week will be your employee. They aren't going to have much time to do other work!
Employers Liability insurance is usually part of your home insurance. Dig out your paperwork and check the policy detail. Most policies include it - if it isn't included contact your insurer and ask what the extra premium will be... given that most insurers include it, I doubt it is that much.
asknannynick.blogspot.com - some info I've gathered together for employers of nannies. It's very much a work in progress... but you will find some things there about Recruitment and Taxation.
Some extra costs to consider:
Nanny using their own car - mileage is 40p per mile for the first 10,000 miles per year. Mileage can add up fairly quickly, especially if you are in a rural location where a toddler group could involve a 20 mile round trip.
Nanny weekly kitty - cost of outings for twins is not going to be cheap. Most nannies are quite good at budgeting and will seek out low cost activities. It is worth budgeting for £20-£30 a week for activities... with that increasing during school holidays as most places charge for a 7 year old to visit.
Nanny will want feeding during working hours. That will likely mean eating Lunch with the twins, also possibly eating high-tea with all 3 children.
Household costs such as heating/lighting may go up a bit - but to compensate for that you will get all the children's laundry done and possibly some light housework such as running the vacuum around on occasion.
A big benefit is having someone take over the morning routine... so you don't feel quite as rushed having to get all the children ready and to their various places before you go to work. Another advantage is that if your 7 year old is mildly ill, so not well enough for school, but not sick enough to need your constant attention - the nanny may still work... so you don't need to take the day off. Nannies will put up with children who have a minor illness much better than a Childminder or Nursery (as group daycare providers have to consider the other children in their care).
Nanny Holiday - your nanny will be entitled to 5.6 weeks paid holiday (this can include Bank Holiday's). This is statutory minimum so should be the same as you get from your work.