If I understand your question, you are looking at connecting the garden hose fitting on the side of your TT to the sewer connection at a full service site. I do not recommend doing that unless you take some precautions. The sink in your unit has a direct connection (without a trap) to the connection on the outside of the TT. Connecting this to the sewer fitting at the park can allow sewer fumes to enter the TT via the hose. You should either rig up a drain trap in the drain hose, or use a container ( 5 gal bucket or portable holding tank) to capture the liquid and dump in the sewer connection when full.
https://www.amazon.com/Barker-Manufa...ng+tank+for+rv
If you choose to add the trap in the line, You can use something like this to seal the sewer connection.
https://www.amazon.com/Camco-39322-W...5G3Y5X93XDQM59