3 things:
1. My thought is that it might be wiser to skip the conversion back to 240V AC and just go with a DC charger. Make a CHAdeMO charger out of it. This will save you the one out of 2 AC/DC DC/AC conversion losses. this adds to complexity and costs, but saves conversion losses.
2. Also keep in mind that Tesla specifically states you should not be charging the car from generators. The charger probably doesn't like nasty sinus or square waves either. So you need to be sure you have a high quality inverter with a true sinus output. Another reason is issue 4:
4. Tesla starts charging slow, and then slowly (in the course of a second or 10 or so) ramps up the amps. This allows your inverter to adapt. When charging is complete, it abruptly stops. In case of a generator or inverter this might cause a dangerous frequency peak. You should make sure there are no other appliances connected to the inverter when this happens and it might cause harm to the charging equipment (Tesla UMC)
When running a generator you can actually hear this happening. When you run a generator and you turn on eg. a coffee maker you will hear the generator adapt. It revs down for a second when you turn on the coffee maker, and it has to adapt and increase fuel injection. During that time the frequency of the output is off. Sensitive electronics don't like that.
5 . You need quite a few batteries to be able to draw a significant of power out of them. Don't know what your required charge rate would be, but to discharge 11 kW out of a battery pack you need quite a few batteries.
4. it is probably a lot cheaper to just get a 240V outlet at the location you want to use this.
@compu85's advise is risky. If the 2 outlets you are going to use are from the same leg you will:
1. Risk making a short circuit (if the polarity of the 2 sockets is reversed)
2. You break the functionality of the circuit breaker if the 2 sockets are behind different circuit breakers.
I would definitely not do compu85's advise on a property that is not yours or where there are other people. You risk lives by disabling circuit breakers or GFCI's and you increase risks of starting fires.
Is everyone going to skip over the fact that he started this off with '3 things:' and then numbered his items 1, 2, and 4. ?