I have a iPhone 5 on AT&T I have the Unlimited data plan I'm still grandfathered in. I just got a iPad mini 4g lte. Would I be able to Install my Sim card from my iPhone to my iPad Without AT&T noticing it.
No, sorry. First off, the SIM wont work in the Mini and secondly, yes, AT&T would notice it [anyway]. People tried this when the iPad first came out - no luck.
When you swap a SIM from one device to another, it won't work unless its an unlocked device (in some cases). Secondly, your SIM will retrieve your ESN and/or IMEI for the carrier to verify or find out which device you're using