I have the Battery BacPac and if I just leave it on, recording every now and then and maybe switching it to photo mode (read: light usage), I'll get 5-6 hours out of it. I've never tested how long it'll run if I just let it go but I've done days where I've recorded several 15-20 minute videos. WiFi is always on (I love the remote) so I have no idea what's up with your's.
Also, you can leave the WiFi on and turn it on/off with the remote. That's what I will do. Turn on the WiFi while the camera is off, and you'll see the blue light blinking. When you turn your remote on, it'll sync with the camera, and it'll turn the camera on. Turn the remote off, and the camera turns off, but WiFi stays on for you to do it again. Do this and it'll last all day, easy!
What settings are you using, as well? That might have something to do with it.