Volts x Amps = Watts
12v x ?? Amps = 1000 watts
1000/12= 83.3 amps
83 amps is more than most car alternators. Maybe in a diesel pickup, RV, etc as those tend to have bigger alternators.
I believe you’ll kill the donor car’s 12v battery pulling anything more than about 50 amps, which is only 600 watts. 600 watts @ 120v means you’re only going to get the equivalent of 5a at 120v. That’s maybe 1-2 miles per hour of charging.
You mentioned your Volt pulling 12a@120v, which is similar to a Tesla UMC on a standard 15a plug (it only pulls 12a).
120v x 12Amps = 1,440 watts.
I wouldn’t pack a 2,000 watt inverter as safety equipment. It’s just not worth the effort and extra space and weight, plus hoping someone will just park their car for 1-2 hours while you trickle charge.
Just pay for AAA or get roadside assistance through your car insurance and call for a flatbed if you’re ever stuck