you are not in the right forum's category. You should post it in LiveCycle Designer for instance.
To answer your request, there are two ways to design it:
1) The PDF form submit the data to LiveCycle (Java service on the server-side) that sends PDF copies to the three recipients.
2) You create a "sned by email" submit button. The user that fills the form will sends the result to the three recipients.
You may also consider Adobe Acrobat Pro if you plan to design small workflows.