For daycare:

My local area costs $600-1000 per month, depending on the age of the child ($1k for infants, $600 for pre-school). If we assume 8 hours/day, 21 days/week on average (~250 working days per year). So each child costs $3.5-6/hr. Recommended staff to child ratio is one per 3-8 children, depending on age. If it's only infants, maximum possible wage (assuming everything else is free) is $18/hr (3 * $6/hr). If it's only pre-school age, the maximum possible wage is $28/hr (8 * $3.50/hr). Preschoolers will need more space than infants, so I imagine a large share of that difference in cost is for space, food, and activities.

So my guess is that people providing childcare make $10-15/hr, maybe a little more if they are overseeing a newer caregiver. This cost is already high for workers, so I really don't think salaries can go much higher without a fundamental change in how care is provided.

I can't speak to nursing homes though, because anything touching medical care is incredibly hard to find numbers for.