Ah, Verizon.
First, to the T-Mobile / Sprint users: we regularly travel out into low-coverage areas with our Verizon phones. We have from time to time brought people along who have Sprint or T-Mobile. I have never had a situation where the Verizon phones failed to connect but the T-Mobile or Sprint phones worked. However, every trip the Sprint and T-Mobile phones "go silent" once we've left the main corridors while our Verizon phones continue well into the sticks. So, sorry, Verizon's network is just unbeaten out here in the West, at least everywhere we tend to go as a family.
That said, we have six lines sharing a 24GB plan right now, and are constantly running into that limit (main source of consternation in the household: "Why are you using hundreds of MB of data while sitting in your room at home???" "I didn't know my phone dropped off the WiFi!").
Switching to Verizon Unlimited would on paper be a no-cost switch ($110/month for 24GB, $110/month for Unlimited) except that the employee discount we have works with fixed data plans but oddly not with "unlimited" data plans. So it would be $20/month more to get (Feb 2017) Unlimited.
These two replacement "unlimited" plans coming tomorrow sound like they will cost even a little more ($5/month more for the single user case, but how much more for the 6-line family case?). I am going to go ahead and lock in the Feb 2017 plan for us. I can always switch to the newer plan if it looks more appealing at some point.
Unless they are manually turning off wifi, the phone should automatically connect back to wifi when entering the house. I have never had that issue, on any of my phones. They always connect back to wifi when entering the house.