The side that receives little direct sun will, sooner rather than later, return to a leggy growth pattern no matter what you do, other than moving the entire plant. The best thing to do is accept its one sidedness - the fact that it is backed by fence should mean that it will look pretty much ok.

Hard pruning success depends on a number of variable factors including specific variety, sun exposure, etc. Hard pruning plus high nitrogen fertilizer will produce willowy soft growth that will have difficulty making it through the winter, and may severely damage the entire plant.

I think hard pruning will be just as temporary as any pruning. It will come back the same way. The best way to get the back to grow is to remove some of the front. That is what is shading the back. If you want a more uniform looking plant, you need to open it up. This results in a healthier plant with good air flow and light getting to all parts. Another trick is to paint the fence (at least that part) white so more light gets to the back.

Also, heavy doses of nitrogen will weaken the plant and may prevent it from blooming. A good balanced rhododendron fertilizer is a much better choice.

Rhododendrons are easy to move. They have very shallow roots. If you could just move it out from the fence, things would improve.