No settling in is required if they have nannied before. Better to hit the ground running, take the children out somewhere so they all have to get along together and not have mum/dad around in the background.
It may sound rather harsh but your children have to accept that someone else is in charge when you are not there, so if you are both there it can be confusing for them.
Write down any routines. Be prepared for some routines to change, as they will change over time anyway. At first sticking to the routine can work well but it may also be limiting - you mention older DC so assuming they are at school then that forms a routine which can't be changed but it will change during school holidays.
Two weeks - far far too long. A day maybe but I would try to avoid that if possible and just have a meet-and-greet session of a couple of hours at say a weekend (and yes, pay for that time).
How much of thinking about having a two week overlap is down to your own anxiety about leaving your children with this nanny? It will be hard at first and you need a form of communication which you can use to keep track of what is happening - for example, nanny could send you a photo, update a milk feed log, you could send urgent messages via text and not so urgent via email, you could use digital calendar systems to keep tabs on events/outings as well as the mileage log (if nanny is using a car).
Two weeks I find is the crunch point when the reality of the job dawns and as a nanny I decide at that point if things are working or not, what needs to change to make it work, or do I leave? So make the first two weeks about nanny being with the children as much as possible without you around, so they get to know each other and start building a bond.