In short, what you want to do is respond to the button events (Z-Wave Central Scene to the device and hence often called "scenes," but those are not to be confused with the Hubitat scene you've created) from the device. There are many ways you could do that, but the easiest way would be to use the Button Controller app: pick your button device, then assign whatever actions you want to the various button events. You just have to know what real-world button tap/hold corresponds to what event on Hubitat.
But it sounds like you have another issue, too. I'm not sure why all the bulbs wouldn't be responding. There are some optimization options in the group (assuming you created it in Hubitat's Groups and Scenes app) that you can try adjusting. For example, if on/off optimization is on, try turning it off. When enabled, Hubitat will skip sending "on" or "off" commands to devices that it already thinks are in the right state, but it that reporting gets messed up somehow, your devices may not be getting commands that would help them reach your desired state. On the other hand, if enabled, you may have less Z-Wave traffic and keep your network happier. You could always try using the bulbs individually in Button Controller instead of the group, too, inserting a small delay between the "on" actions as a workaround if really needed (shouldn't be, but if it works...).
Finally, make sure you have local control disabled on the dimmer (or, equivalently, local protection enabled). You can do this by using the option in the driver (if the driver you're using exposes one) or by tapping the config button 8 times to toggle this setting (if it flashes red afterwards, that's what you want; green means local control will again work, something you won't want for smart bulbs). I'd also enable the "smart bulb mode" parameter (Inovelli's driver exposes this; Hubitat's doesn't), though I think just keeping the bulbs at 100% (or Z-Wave level 99), so not accidentally adjusting the dimmer (which again local protection would help with) should do the same.
PS - What model hub do you have? If you're not sure and bought it recently (since July), you probably have a C-7. The Inovelli bulbs, I think, use a type of Z-Wave security called S0. On the C-7 hub, they will pair as S0 automatically. This can be chatty and might be the root of some of your problems, but unfortunately, it's very difficult to pair them without security on a C-7 hub, and they don't support S2 (the newer kind of security, which is less chatty and should generally avoid this problem). On a C-5 and earlier, you can pair them either way, but the default is non-secure.
