The fact that they can't load balance is an issue beyond their control as far as they are concerned.
This is your main issue. If they installed it like that without reading the obvious instructions, with the possibility over overload on a 240V circuit I would think is against code. The fact that it burned your hand is not just a human hazard, but a REAL fire hazard. I don't think Tesla has done anything wrong here, but surely your electrician has. They are the ones who "assumed" it would work, and since they are the professionals and paid to RTFM, they are at fault, at least IMHO. At the very least, they should come out and re-wire the G3 charger to it's own breaker so you don't overload that 60A breaker, causing it to heat to potentially the point of fire. If you have the spare capacity in your main panel, there should be no issue.
In the end, the electrician should have quoted you either:
1. a dedicated run from the G3 charger to your panel (mimicking your G2 charger)
2. install a sub-panel between the main panel and your G2 charger, allowing you to branch to both the G2 and G3 chargers.
3. return the G3 and search online for a G2 charger (you see them all the time for sale on this community).
1 and 2 likely would cost more than your initial quote in both hardware and man-hours so if they end up going that route, I do think you should be on the hook for the difference. However, since they put your house in an obviously unsafe, and potentially against code situation, perhaps they can knock something off the labor rate. I would be very nice with them but if they get to a point where they are being unreasonable, politely mention you might want to ask your local authority to "safety check" the installation. Be careful here as I don't know all the local regulations and if you/they were supposed to pull a permit first.