Regardless of your home set up, a 2 or 3 day a week nanny is very hard to find and even harder to keep.
We have a perfect, full time Mary Poppins nanny and have since my 3 yr old was born. We adore her and she’s shown me the value of nanny-care. I encourage all my friends to get great nannies. But in your circumstances, OP, I would recommend daycare.