Online class cheduling

As a Red Cross volunteer I am seeking a solution for a health and safety class scheduling problem. We recently merged two Chapters into one but still maintain two offices in different towns.
Both offices currently maintain student scheduling books for a single set of classes leading to frequent mishaps to say the least.
I would like to set up an online scheduling system which would be accessible from both offices which would allow both offices to entsr signup data for students into any given class, save the entries and then allow the data to be added to, edited or subtracted from any location.
I can do the .html forms. I can email the entries to either office but can’t find a way to make it truly interactive.
My online searches would suggest that what I am seeking simply is not possible. Are there any contrary opinions. Thanks