So here's how wireless CarPlay works. TL/DR: It operates via a discrete wifi; your phone cannot be connected to two different wifi networks simultaneously.
Turn truck on
Phone pairs to truck via bluetooth
Truck sends bluetooth signal to phone saying, "Bro, why don't you go over here and join my discrete wifi. Don't tell your friends tho."
Phone connects to truck's discrete wifi; Apple CarPlay operates over this discrete wifi
Phone does not display a wifi signal at all
Discrete wifi (i.e. CarPlay wifi) and the truck's 4G LTE WiFi are two separate networks
Phone displays the cellular data network to which it is connected. Your cellular data network is how your phone gets data, and in turn, how any services work (i.e. streaming content, such as Pandora) on CarPlay.
You can't connect to your truck's wifi and run wireless CarPlay simultaneously because your phone can only be connected to one wifi network at a time.
Some thoughts. First, your truck's wifi is basically a cell phone data plan turned into a hotspot. So, it'd be like using your cell phone to create a hotspot, then connecting all your family's devices to that hotspot. Know what'll happen? All your devices will have slow data, because they're going through only a single hotspot which has limited bandwidth. If your devices have their own cellular data plan, they'll be much faster using that versus all connecting to the truck wifi. You should really only use the truck's wifi for devices that don't have cellular data. Second, even if you could connect your phone to your truck's wifi AND run CarPlay simultaneously, you wouldn't want to due to limited bandwidth (see first thought).