I'm in MN ~ the mosquito capital of the US.
I require parents to supply sun screen and bug spray if they want their kids to wear it. (Sun screen is a MUST).
We are outside most of the day in the summer. We go outside alot in the winter as well but we spend 90% of our day outside in the summer months. We often eat lunch and nap outside too.
The way I see it is if the mom doesn't want her kids outside she needs to find a child care that stays inside all day or she needs to come pick them up when you are taking the other kids outside.
You do what YOU need/want to do. It's YOUR business to run not hers. If she isn't happy, she needs to find a program meets her needs/wants.
I wouldn't worry about it.