The only thing you can do is divide up your loads so that you can put some on one inverter and the rest on the other. Then the two inverters CAN be hooked up to the same power source.
Just remember that 1000W @ 12V = 831/3 amps. That'll draw a standard car battery down in a little over 21/2 hours (455CCA batery dropping below minimum voltage, not completely dead). And even if your car is running at the time, most cars only run a 35 - 55 Amp alternator. So all you've done is delayed the inevitable.
As I found out the hard way. I was running my 1600W inverter off my truck, which was idling. Now, it has a GM 105A alternator, but with the truck idling the alternator couldn't put out full power. So after running my saw for a couple hours, my truck sputtered to a stop. I thought I'd run out of petrol. Come to find out the battery had gone so flat it didn't have enough power to fire the ignition coil. I had to take the battery out of the truck and carry it back to the garage to put it on the charger (for 24 hours it was so dead).
So please be careful as to what you hook a 1000W inverter up to.