I have this - 2 days a week arrangement. As a PP said, I'm still an employer. My nanny works 3 days a week for another family. I know them, but we're not a 'nanny share' - we're each separate employers.
MOST IMPORTANT THING! - You MUST advertise and agree a GROSS rate of pay, not net. Otherwise you will be in a massively complicated tax situation which will drive you insane and may cost you a lot. If it's a gross pay, there's no issue.
I use a nanny payroll company which makes it even simpler, and hired my nanny via an agency.
There are lots of part-time nannies in my area - not enough full-time jobs available I suspect. The only awkward situation is when your nanny loses her other job (family move/don't need a nanny any more) - if she has trouble replacing it, it can end up in disruption to you (if she goes to another job).
I've had my nanny for 3 years, and hopefully will much longer. I give her regular pay rises, and I've told her that if her other family give notice, then to talk to me before she does anything rash - e.g. I would consider employing her full-time while she finds another part-time job to fit with us, rather than risk losing her because she needs to take something else quickly and it doesn't fit with our days.
Also - another important thing. Think about all the jobs you'd like your nanny to do (esp if the role may change over the years). Our nanny does ironing (for the whole family not just kids), changes beds (ditto), runs errands etc. etc. Next year all the DC will be at school, and she'll take on more household tasks like cooking family meals etc. in term-time. She is very happy to do this, and it works well - but many nannies wouldn't like this kind of role.
Also think about your particular requirements (e.g. my DC have special dietary requirements, I have a no-TV in the daytime rule etc. etc.) The more you discuss up front, the more you'll both know if this is a good fit.