There is a "Tesla Camping" group on the Facebook that is fairly active. Many talk of towing trailers there. The short answer is, expect your range to be cut in half, maybe slightly less with a teardrop but still plenty. And no, many national parks are a bit sparse with charging, though some are OK with it. Towing is doable but it's one of the things that ICE cars do better for now.
Of course the good thing is you can stay at RV parks with 50a service and recharge your car there. Though there is a minor challenge of plugging in both your car and your trailer at the same time. However, since you probably won't run your AC at night, you can probably get away with plugging the trailer into the 15a plug (though it's probably 20a) and dialing your car down to 30a and you will still refill all but a model X and not blow the breaker. You can now dial your car down in the app. You might dial it down before microwaving, that and the AC are the only things going to draw more than 10a. In the future you'll get a device in the trailer that measures how much it is using and automatically dials down how much current the car takes so it can take full power once you get to sleep. If you really worry, and the rv park is sparse, bring a 12AWG extension cord and plug the trailer into the next pole and your car into the 50a plug to get the full 40a (if you have a long range.) Probably no AC that way, though. Clear it with the park.