If you have a nanny you are also not doing what a Sahm of preschool children does, or else you wouldn't have a nanny!
I'm always astounded that people feel the need to put sahms in their box by claiming to "do everything they do plus work". Why? The only way anyone asking a sahm of preschool children role and working is if they look after the children, entertain, nurture, educate, socialise, clean, nurse and feed them at the exact same time that they do paid work. As well as the rest of the domestic and cleaning load obviously.
Even if you work from home, you're not doing what a sahm does unless you work and do childcare simultaneously, and if you have a partner they only do the same share of childcare they'd do if you were a sahm (so say 50% of evenings and weekends and night waking at most).
Some people manage part time work from home or shift work on that basis, but to work full time in a paid role would only be possible if you didn't need to sleep (not just as a hyperbolic figure of speech way, but in a physically lethal within 3 weeks way) or neglected all but your child's most basic physiological needs while working (which would anyway mean you were not doing what a sahm of preschool children does, unless she's very unwell!)
Cleaning is part of being a sahm, but most of it is nurturing, educating, socialising, and caring for a child or multiple children all of the time.
On the other hand the way to keep your shit together during those years is to take the kids outdoors as much as possible, not own too much "stuff", and lower your housekeeping standards.
I work now and come home to 3 school aged children. Being a sahm to preschool children is harder than working full time and coming home to children who are with other people all day.