When network goes offline, phone won't switch to data - why?

[AC Question]

My home internet connection is unreliable sometimes. The WiFi works fine. When I'm at home, if my phone is connected to the WiFi and the internet connection goes out, my phone won't use my mobile data connection to connect to the internet unless I manually turn off the WiFi. Is there a fix for this? I would like it to automatically switch to using the data connection whenever the WiFi internet is down. I have looked for apps to do this but haven't found one that looked good. Any advice?

 

[pookel]

(Original author here, created account to add followup): Phone is a Droid Mini using Android 5 on a Verizon 4G connection. However, my previous phone was a Droid Razr M running Android 4.4, and it had the exact same problem, so I don't think it's phone-specific.

Please don't tell me "it's the WiFi, fix the WiFi" because what I want is for my phone to switch to mobile data whenever it doesn't get internet over WiFi. I'm stuck with unreliable internet (and at work, unreliable WiFi) so I'd like my phone to be able to deal with this.

 

[pookel]

Anyone?