Well, you still got plenty of cash for razing those cities, so I wouldn't worry about it.
Go ahead and finish off Roosevelt and Catherine, then repair your economy.
For an industrial-to-modern era Domination Victory, your ideal Civics combination is Police State - Nationhood - Emancipation (or Slavery) - State Property - Theocracy (or Free Religion). Universal Suffrage can be useful when you are preparing for war, but once War Weariness kicks in, Police State is required.
You will need plenty of Jails, and you should build Mount Rushmore as soon as you have a chance. Police State + Mount Rushmore + Jail = zero War Weariness. Until you reach that point, you may find yourself needing the culture slider, so Theaters and Coliseums (and broadcast towers, when you get to Mass Media) are also nice.
Phase I of your push will be with Artillery, Tanks, and Infantry. When you learn Flight and Radio, build Bombers and a few Fighters, and STOP building Artillery (air replaces artillery).
Build Airports as soon as you learn Flight. Airports allow you to airlift units into newly captured cities, and will greatly accelerate your conquest.
Once you get into the modern era, your key units will be Stealth Bombers, Modern Armor, and Mechanized Infantry. If your opponents mount any kind of defense, you may need to invest in counters (Jet Fighters counter Jet Fighters, Gunships counter Armor, SAMs counter Gunships, etc).
The battle for any city follows the following formula:
- Bombard defenses (don't forget that air and sea units can do this, too!)
- Collateral Damage (artillery, bombers, and barrage-promoted armor do this).
- Clean up (drill-promoted armor are best for this)
- Garrison (1 or 2 Infantry/Mech Infantry should be enough).
- Heal up, rinse, and repeat.
Hooray! You have now achieved Domination Victory!
), so the AIs will be hindered
