Homebase and Unlimited Plan

Hello!

So, I live out in the country with my family, and in addition to our phones, we have an old AT&T homebase that we use for our internet. It runs through our unlimited data plans on our phone, taking from the same pool our phones use to give internet to the whole house. It's an older model of homebase, we've been unsure if we should upgrade as we can't find any information the newer ones would use our unlimited plan the same way.

My question is though, that my family and I are looking to maybe switch our phone plans over to a different carrier, and we are wondering if its possible to keep just the homebase as its own line (it is shown as a line in our account information) and still have it with unlimited data. Could anyone point me to some information on this? I tried calling, but the automated service just took me around in circles.