Hello Manav! It is so exciting to hear about your involvement with your local school and your passion to make a difference in the education of young children in urban slums. Your idea of using existing school infrastructure is great.
In British Columbia, Canada we have identified public schools as an important part of our community infrastructure and a place for innovative early childhood programs called Strong Start. ( "The overall learning is shared as parents and caregivers attend with their children and are encouraged to get involved in activities like telling stories, playing games and serving healthy snacks. Join us to learn new ways to support your children’s learning, get information about community programs and services and make valuable connections with others attending the program." Source: http://www2.gov.bc.ca)
Have you considered a whole family approach at least initially to help families feel welcome at the school and part of their children's education. Perhaps focusing your age group on the 1-5 years in the context of social interaction and learning through play would be doable.
I also love the concept of sharing amongst families--supplies and clothing-- made available to children who may need these items. I have seen lovely examples of this type of approach work in several "Community Schools" in Surrey, BC. Thank you for inviting me to comment and contribute in shaping your wonderful ideas!