O.K., I am certainly no expert, but I need to understand a few things -
(1) This is not gmail, right?
(2) Is the ISP for your home the same as your e-mail provider (in other words, do you have comcast, and is comcast.net the e-mail service, or at&t and att.net, etc.?).
If it works on 4G on your Rezound, have you tried making sure the settings are the same in the Thunderbolt?
That's all that comes to mind. Or do a factory reset, mw everything away, and start from scratch. It sounds very much like one particular setting is not right, but I can't tell for sure what that might be.
BTW, my wife refuses to set up her non-gmail personal e-mail onto her Incredible 2. And the only reason she has gmail is to get the App Store Play integration.