Your Tow Vehicle is pretty short. As long as the tow vehicle can make the turn, the trailer should follow. The right side trailer tires might go over the grass near the street. Maybe leave your weight distribution bars off while you make this maneuver. Just don't jack knife if you have to back up a few feet so you can make the turn tighter.
Personally, I go to the RV lot. Hitch up my 35 5th wheel and park it in front my house. I live on a dead-end street. To get out. I pull forward centering my rig in the middle of the street with cars on either side of the street. Then back down the street a few houses until I reach the intersection and turn the rig 90 degrees onto that street. My wife stands at the intersection and waits for a break in traffic then has me back up, then stops any other traffic that approaches. You should be able to do similar by pulling directly across into the alley. You are a bumper pull, so your TV should offset less when turning than when towing a 5th wheel.
You have a another choice. Put a receiver on the front of your tow vehicle. You can make a really tight turn if you hitch up your trailer to the front of your tow vehicle. I have a bumper pull and have had to do that once or twice backing in my bumper pull trailer into our driveway when the street was lined with cars.