If I wanted to be sure things would be cool for the dogs:
1: I'd go for a Magnum Energy or Victron "hybrid inverter". Voltage too low? It will suck on the batteries to make up for the lost electricity, and not burn out the windings on the A/C compressor.
2: As above, I'd go for a Fantastic Fan 6000 series model that has a rain sensor, thermostat, and works off the 12 volt system. A 7000 model is stronger, but requires 120 volts.
3: If you have the space (probably not an option) perhaps consider taking a portable A/C that vents out a window? This can either be set at the same temperature as the roof A/C so both are working, or it can be set higher as a failsafe.
4: I've seen alarm systems for K-9 cars that first warn at a certain temperature, then will pop the door open to let them escape. Yes, runaway animals are bad, but better a pooch hunt than dead dogs.
Don't chuck the old A/C. It was made before most parts and components started coming from the absolute cheapest country with the least amount of regulation and quality control. It also uses far better Freon than the current refrigerant in use, so the compressor has to work less for better results.
In fact, avoid chucking any old appliances unless they break in a way they are unfixable. A friend of mine has a RV with a refrigerator that does not use a control board or 12 volts, so no matter how discharged the batteries get, his food remains cold, assuming it is set on propane.
