Why not just simply refuse to allow the younger child to stay for the day if she doesn't have the required clothing?
Rather than be so judgmental about this mom's feelings/words, just continue to do your job and enforce your policies.
I get and understand that we "know" the parents in our care but we really have never walked in their shoes or lived their lives so I refuse to spend my time and energy judging and just do what I need to do as far as business goes.
If you require ALL children to have certain clothing to go outside in, then stop allowing the parent to drop off any child unless they have those items. If DCM decided to stop coming or find other arrangements because she can't live by your rules, then that is her choice.
I just do my job and not worry about the rest.