There's a couple things you should look into here. First, don't trust what the screen tells you for power, since you don't necessarily know what data is being measured, or to what accuracy the value is measured. We know for sure the car doesn't show values below 1kW and that it doesn't display fractional values, but that's about all we know.
First, if you're not comfortable with these steps, or know what they mean,
pay a professional. You can kill yourself instantly, so don't risk it.
Get a voltmeter and ammeter. You can get a combined device, and non-contact versions exist, though for voltage testing you need to use probes to do it right.
- Test the voltage between the two hot legs. The value should be within 3% of 240v.
- Test the voltage between each hot leg and ground. The values should be within 3% of 120v.
- The maximum voltage drop should not be more than 5%. If it is, it violates the NEC, and it could be a clear cause for your problem.
- Clamp the ammeter around one of the hot legs before the HPWC. Plug the charger into the car and observe the measured amperage.
- Clamp the ammeter around the other hot leg, and repeat the measurement.
- These values should not measure over 40A.
- Measure the temperature of each leg with a no-contact IR thermometer after the vehicle has been charging for a while.
- If the breaker trips, measure the temperature of the breaker in the panel with a non-contact IR thermometer, as well as the feeder wires.
If your voltage drop is over 3% or the feeder/branch wire is getting hot, it's very likely that the circuit was not installed with the proper wire gauge somewhere between the panel and the HPWC.
This can cause a fire. Wire is rated for temperature ranges, and if yours is getting hot it can melt the insulation off, short out on the conduit or inside your walls, and someone could get hurt or die. Nobody should be messing with an electrical circuit that doesn't behave properly.
If the voltages measure properly, the ammeter doesn't read above 40A, and the hot legs in the circuit aren't getting temperature hot, then it's just as likely that your breaker is garbage and too sensitive. The fact that your other Tesla doesn't cause this issue can be attributed to a million different variables that we simply don't know without detailed measurements being taken. Either way, if there's something wrong with the circuit, please stop tempting fate. People lose property and die due to electrical fires, and it's not worth the risk. Get an electrician to look at the circuit, tell them what you're trying to do, and let them make a recommendation to you.