Different floats for mobile and desktop version

We have the issue that the badge we install and configured for desktop looks too heavy for the mobile version with the companys icon added. The other way around, to create it ‘mobile-first’ it looks poorly on desktop, with the icon missing.

We tried to create two floats, one for desktop (‘Do show on mobile – no’) and another we wanted to use for mobile, which commes lighter. On mobile we get what we wanted, but on desktop we have both in display.

Is there a way around? Maybe to with css?