Based on your pictures, it appears that you need a right hand door lock. You will need to remove the 4 bolts on the inside of the latch to remove the cover plate and measure the size of the cut out in the door to make a good choice.
The Bauer BA76FR that you referenced is no longer available, but I have another good choice.
The Global Link # 295-000183 keyless latch for trailers fits a 2.75 X 3.75 inch right-hand opening.
The Global Link # 295-000185 keyless latch for trailers fits the... view full answer...
The Go Power Industrial Pure Sine Wave Inverter Charger # 34275013 that you referenced does have the ability to charge lithium batteries like you have. I would recommend using the custom settings like you mentioned to match just what the battery manufacturer recommends. view full answer...
The rear sway bar you want for your 2015 Coachman Pursuit 31DB is the Roadmaster part # RM-1139-146 which I attached an install video for on a similar Pursuit and then for the front you'd want the part # RM-1139-148.
For the Ford F-53 chassis that your RV has you'll see the biggest improvement with the rear sway bar but the front will help a lot as well. Doing both will make a huge difference. We do not have them as a kit. view full answer...
We do have travel trailer door latch/locks that have keyless entry like the Global Link Ultra E Pro part # 295-000183 for a right hand style or the part # 295-000185 for the left hand side. These have a dead bolt on top as well. If you order more than one you can have them keyed alike as well. view full answer...
The Go Power Industrial Pure Sine Wave Inverter Charger # 34275013 needs to have power ran to it and the button to turn it on must be pressed with the light on the display to show that it is on. view full answer...
In order to verify that your RV can safely pull your Chevy Tahoe, I recommend contacting the RV manufacturer directly for its specific capacities. If you provide them with the RV's VIN, they should be able to give you its exact limits.
If you find that you can pull your Tahoe, you will need a base plate kit, tow bar, safety cables, lighting solution, and a supplemental braking system. You will also want to check the owner's manual for your Chevy Tahoe for any specific guidelines or restrictions... view full answer...
You can mount the Curt friction sway control unit part # 17200 on the passenger side of your trailer. You'd just need to remove the insert from the housing, rotate it 180 degrees and then reinsert it and you'd be set. view full answer...