In my specific context, should I always put press the HV button when in driving so as to fill up the battery as much as possible?
Absolutely not. HV charge mode is the least fuel efficient mode there is. Just be diligent about finding charging stations wherever possible. [...] So you could just drive the car as if it were a hybrid and plug it in when possible. That just seems to me to defeat the purpose of a plug-in hybrid, though.
To expand on this:
HV Charge mode is useful for one thing and one thing only: You have an empty battery, are driving for a while and will not be charging, and know you're about to go up a mountain. That's it.
Chevrolet
much more helpfully called the same feature "Mountain Mode" in the Volt. You should use it when you have no charge but want some reserve that you will use driving up a long, steep hill that the gasoline engine alone may not be able to handle at highway speeds. Period.
Regular HV mode (not HV Charge) just saves around whatever battery capacity you have, so can be used to manually switch from using gasoline to the battery.
As far as how to drive your car in normal use (I'm assuming here you live in a city or at least not somewhere unusual like on top of a mountain) it's really not complicated: Leave it in EV mode and plug it in whenever you can. If there's charge, it will use it. If the battery is empty, it will switch to HV mode as necessary. That's it. Depending on how much you drive and how often you're near a charger, you might actually end up in EV mode most of the time, since you can put 40-50 miles of range in the car in 2 hours at a Level 2 charger, which are easy to find in some cities.
If you
really want to spend effort manually managing energy use, you
could, optionally, manually switch to HV mode (not HV charge, just HV) when you have some energy in the battery, are driving at highway speeds, and know you will be running out of battery before you next plug in. The gasoline engine is somewhat more efficient at highway speeds (due to the mechanical transmission that kicks in around 50mph) than at slow speeds, while the all-electric drivetrain is more efficient at lower speeds
But again, that's only if you have some charge in the battery and know you will be using more than that much before the next time you plug it in. If you have 30 miles of range and will only be driving 20 miles before you plug in for a couple hours at a Level 2 charger, just drive in EV mode. If you have 30 miles of range and will be driving 60 miles before charging, 30 of which are on the highway, before plugging in, you'd do better to put it in HV mode for the highway miles then switch to EV once you're going slower.