This device will not assist you.
While it is possible to create a device that will change 120v to 240v, you get a corresponding drop in current (amperage) by doing so. It's a wash. Additionally, the process takes away some of that current, so you actually do worse using this device. The fact is that a 120v outlet can deliver about 15 amps, and you can't change that by increasing the voltage from 110v to 240v. The amount of total current is the issue and that is not increased in this process.
So, you need a connection capable of more current. One possibility is to connect to an actual 240 line, which is generally capable of delivering 50 amps, rather than only 15. Older 240 lines were generally only 30 amps of current. These connections have different plugs. (14-30 v. 14-50) You can plug your Tesla adapter into the 14-50 outlet if it reaches. You can get extension cords for that type of connection. They are not cheap, but they are available. Do what you can to get a good one if you go this way, because that is a lot of current and you don't want a poorly constructed cord that can overheat and cause a fire. Tesla discourages doing this for that reason.
Consider patronizing businesses with commercial grade connections, such as restaurants and local malls during your vacation. Consider an occasional trip to a SuperCharger.
Do some math and see whether a 110 volt connection might suffice. You will get about 3 miles of range per hour of charge. If your car will tend to sit from 9 p.m. to 9 a.m. most nights, you'll get perhaps 35 miles of range each night. That MIGHT get you through much of this.
And if this just isn't working out, consider renting an ICE car, painful though that might be.
