I assume the phones are AT&T-compatible.
The issue is probably with incorrect APN settings - all you need to do is create a new APN having the proper stuff - and you can find the values online.
You can't just put the ATT image on AFAIK - or not an official one. You have a VZ phone, which is a different model#, and even if it's 100% identical otherwise the update may barf since it sees a different model than what it expects.
In addition ATT/VZ/TMo/Sprint models have different bands enabled - sometimes it's just in the modem firmware, sometimes the chips may be different.
Personally I no longer buy carrier-branded phones. I buy factory unlocked and unbranded and it's guaranteed to work with all.