You should assemble a charging kit that you can rely on for charging at the summer camp locations. Start with the Tesla Mobile Connector kit that comes with the Tesla vehicle. The kit includes a NEMA 5-15 power plug adapter. That will work with any grounded 15 amp or 20 amp 120V outlet. If you want add to the kit then consider a NEMA 5-20 power plug adapter.
You can purchase additional power plug adapters for the Tesla Mobile Connector from the Tesla Store (either individually or as a set.) True RV campgrounds commonly offer a 30 amp receptacle known as a Travel Trailer 30A (TT-30), a 120V, 30 amp outlet. Tesla does not sell a TT-30 adapter but this can be purchased from EVSEadapters.com.
You will want to add a contractor grade three prong extension cord, or several. A shorter cord, up to 50 ft. can be 12 or 14 gauge. If you also decide to bring a longer extension cord, up to 100 ft., it should be 10 gauge or 12 gauge. Only use an extension cord if needed, use the shortest length extension cord that can reach the electrical outlet. Do not daisy chain the extension cords together.
Tesla provides a table that can give you an estimate of how many miles of EV range are added per hour of charging with each type of 120V or 240V circuit when using the Tesla Mobile Connector.
Gen 2 NEMA Adapters
The Tesla vehicle also comes with a Tesla J1772 charging adapter so you can use any Level 1 or Level 2 charging station (some require an account, others are free.) Download the Plugshare app onto your phone to locate public charging stations near your location. Use A Better Route Planner on your phone or on the web to help plan your trips, determine charging locations.
I would use the Tesla Supercharger network when you need to charge on the road. Although using the Supercharger network will cost perhaps $0.30 per kWh (some places a bit more or a bit less) using a Supercharger will save you time. I would not be concerned about the Tesla's battery pack when Supercharging. The Tesla vehicle will manage the charging session to protect the battery pack.