Nannying and a newborn

Caitlin • Here we go with baby #3!
I work as a nanny, with three kids 8, 9, and 11. I was under the impression, after I started nannying them a couple months ago at 21 weeks, that I would be able to bring my newborn with me to work. It was something they had offered their previous nanny and she turned down after giving birth, and something we had talked about during my interview. 
I personally think I can handle it. Women go back to work quickly after giving birth all the time. The mom just looked at me and said "yeah, but that's without a newborn. Newborns present another set of challenges." She also kept saying "I don't know if you can handle a newborn and three kids." It's all a bit upsetting considering I was planning on staying with the kids after giving birth, since they have had such a change in nannies over the past two years. 
Do you guys think nannying with a newborn isn't possible? I know I have a bit of driving to do with the kids and running around but it's a split shift, small morning shift of 1.5hrs and 4hrs in the afternoon except on half days, when one of the kids is sick, or no school. How can I show her that I can do it?  
I also told her that if I don't work for them, I would be working for another family considering I can't afford not to work, not at this time. 

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