Been searching feverishly on this topic and can't find much out there so thought i'd reply to this.
The other day, my boss comes up to me and says when he emails all invitees from a calendar entry, it goes out through his personal email address - not his default corporate address. I replied "how are you emailing all invitees?". Then he goes on to show me..open a calendar invite, click on the group of Invitees, and then click THE ENVELOPE ICON on the upper right of the Invitees list screen. Baffled, I check my phone....as suspected, NO envelope icon...just a list of the invitees. To duplicate his configuration, I added a personal email account to Mail (normally I use Outlook for personal mail, and the Mail app for corporate). Viola! Now the envelope icon appears and I can indeed email all invitees exactly as the OP (and me!) want to! BUT, the email is sent through my personal email account and not my default corporate account.
Not sure exactly what's going on here. In searching the web, I can find no mention anywhere of an envelope icon on the Invitees screen, let alone how we might solve the problem of the message going out through a different account.
Running iOS 10.2.1 by the way.