These are great ideas. I think the best messaging system could be determined by talking to parents at each hospital. Every context is different. Most parents could want Facebook, texting, emailing, or a 24 hour phone line.
I think the usability of Facebook groups depends on the number of people in each group. Another way to limit spam is to set up some guidelines for the group, so group members know what the group is supposed to be used for. You could also create very specific groups, so that members are invested in those groups and limits the number of people in them. For instance, an "Allentown Fathers of November 2017" group, or something similar.