I think that there might be some confusion here. Your smartphone is basically a mini-computer that can connect to the internet using either WiFi or a 4G network. (So, for example, you can visit AB, access your email account or log into Skype with either type of connection). However the actual phone app on that mini-computer needs to be able to connect into the 4G network so that, for example, Three's 'virtual telephone exchange' can recognise the phone number that you're calling and route it accordingly. Just as you can't make phone calls with your phone using your home WiFi network (other than via Skype, etc), you wouldn't be able to make them via a MiFi device.
If you're getting a lousy signal with the Three network, you need to switch to a different one. Unless you're constantly playing video games, watching (or uploading) countless YouTube videos or using your phone to watch lots of Tv programmes via iPlayer, etc, you almost certainly won't need anything remotely close to 60 GB of data per month. The 12 GB I get for a tenner a month with Asda Mobile (which uses the Vodafone network) is vastly more than I ever use and I'd be surprised if many AB members ever use that much data too. (GiffGaff, which uses the O2 network, offer a bit more data for a tenner though, with 15 GB).