Group chat iMessages now being received through email
Someone's phone decided to switch to SMS or MMS, as evidenced by the @vzwpix.com return address—this is a domain used by providers to gateway SMS/MMS to/from email.

I routinely run into a similar issue when attempting group messaging with people with phones from other manufacturers, but it's also conceivable an iPhone may choose to do this if it cannot access iMessage temporarily, e.g. if there was no data connection available.

To prevent this, it's probably best to use an entirely different chat service rather than try to match up the disparate capabilities of phones.