Is it possible for bacteria to acquire family-wide antibiotic resistance?
The two amoxycillin formulations you mention pair the amoxycillin with a Beta lactamase inhibitor. This is because of the prevalence of resistance to beta lactam drugs including amoxycillin. If we were to invent a brand new never before seen beta lactam drug and started using it irresponsibly, there would probably be resistant bacteria within 5 years. The same beta lactam core structure that makes the drugs work against the peptidoglycan synthesis machinery make it susceptible to attack by beta lactamase. A new beta lactam could avoid the lactamase for a while, but the same evolutionary pressures that selected for resistant mutants against the other beta lactams would select for mutants resistant against the new one.

The same goes for the fluoroquinolines you mention. Their mechanism of action is different, they inhibit DNA synthesis by blocking topoisomerase II activity. But once a bacterial strain is selected for that has resistance against one member of a class of antibiotic it's relatively easy for it to acquire the mutations that confer resistance against other members of the class. Changing the structure of the drug enough so that cannot be defeated by the mechanism of resistance while retaining the drugs mechanism of action is probably impossible, or at least we haven't done it yet. Even vancomycin, one of our most powerful antibiotics, has some bacteria resistant to it.