A new exhibit opening Saturday in Coney Island brings to light a bygone era when the seaside neighborhood was instrumental in saving the lives of hundreds of thousands of immigrants. From the 1870s to the 1920s, immigrant women and children would come to live in nonprofit summer homes to escape the disease-filled tenement houses of the Lower East Side and elsewhere. The immigrants, many of whom were sick, would come to the neighborhood for its fresh air and would see their…