I know I'm late to this party, but why can't you simply cut the fence at the top of the parking lot giving direct access to the road? It seems inefficient and potentially problematic, to be driving all the way around a pond everytime you wish access to the back area. You could simply fence off the entire section for cattle and have the gate access for driving, should you need it.
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The road there is only 15' wide. Property fence on the north side of it. Can't really move the fence on the parking area south either as the chutes going to the working pens are right by the tree to the left of where you drew the gate. To back up to the chute you are right by the fence. You could likely make the turn in a pickup but not with a trailer or tractor with implements, or my full size tandem dump truck unless the gate was really wide. Heck I even back my 53' flatbed up on the road south of the pond to get it out of the way when we are regrading the gravel parking area.
The fence has to go around the pond to allow the cows to get to the south east part and in doing so it forms a road.