Couple things....the TT takes 30A, but you really only need 30A to run the a/c. If you are just plugging in to keep the batteries charged, then 20A would be sufficient.
100' is a long run, if you want to draw the full 30A with less than the recommended 3% voltage drop, you need #6 wire.
Again, if you plan to run the a/c in the trailer, then I would put the convenience outlet on a separate circuit so you have the full 30A available for the trailer.
Technically you can run a shared neutral for both circuits, but only if circuits are on separate phases and have a common trip breaker like this. Note that this is the same breaker that would use for a 220v circuit (like a dryer) but can be used to power two separate 120v circuits using a shared neutral.
The problem is you wind up supplying 30a to a 20a convenience outlet, and that doesn't meet code.
A better alternative would be to use a box like this on your post:
(click pic for link)
The breaker limits the current on the convenience outlet to 20A and also provides the required GFCI protection for the convenience outlet.
Then you can run 6/3 UF cable (
not NM), or go with 4 #6 THHN conductors (black, red, white, green) in a 1" plastic conduit, use the 30a common trip breaker shown above, then you will have 2 circuits at the post, virtually no voltage drop on either, and the whole set up will be code compliant.
The other option is just run the one 30a circuit for the trailer, and use the outside outlet on the trailer as your convenience outlet. When we lived on LI I ran 8/2 about 50' and mounted one of these on a pole:
I used the TT outlets for convenience outlets. One 30a breaker, was a lot simpler, and worked for me since I hardly ever plugged anything else in out there except for the buffer when I was waxing the trailer.
Either the cable or conduit needs to be buried 18" deep, so I would definitely recommend renting a trenching machine, then have then at Mid-Island Rentals in Middle Island.