Put a cup of laundry detergent down the stool, and add about a 1/2 tank of water. Take the trailer for a drive so the soapy water can work it's magic. Go dump the tank, then add soap and water and let it sit far a day or two. Go dump again and refill tank with water at the dump station. once full dump it. You said you have the clear coupler on you hose, so you should see cleaner water flowing. Then add 5-10 gallons of water with soap in tank and take it home. ALWAYS put water in the black tank after dumping.
We use the about about 1 cup of the cheapest powder soap we can buy in the tank after each dump.
Also never leave you valve open when you have sewer hookup, the solids will stay in you tank and the liquids will flow out. when dumping make sure you tank is at least 3/4 full before dumping, you need the water to get the whoosh factor to help push every think out. Been there done that with, don't want to do it again.