That is a very narrow alley. There is a 'blue italian columnar type conifer that is like a skinny pyrimidalis,but I am not sure if it would get enough sun there to thrive. Don't plant Photinia or English Laurel for sure.
Since you're that close to the property line, why do you even want that side of the patio open?
Could put up an opaque screen with a semi transparent siding for light but to block the view.
A compromise for privacy.

That's a pretty narrow space. Italian cypress would do the trick, but it will need time to grow in, even though it's pretty fast.

You might think about putting up a trellis and planting a vine on it for faster privacy.

You can also get garden screens. I see screens made from split bamboo that people use to augment fences.

Thank you for your help. I think a trellis fence would work. Just out of curiosity...if 3' wide is too narrow. How wide would I need to plant a hedge, say like a boxwood hedge? Thanks again.

You could put up some lattice and grow vines on it. Autumn clematis and climbing hydrenga have worked well in my afternoon shade area.

Thanks Treepalm. I love clematis, and climbing hydrangea. I think this just might work. I appreciate everyone's help on this. I'm going to google Autumn clematis because I don't know what it looks like. Thanks again.

Try googling Clematis ternifolia or Sweet Autumn Clematis. It may not bloom as well in more shade than sun, but you could try Clematis armandii. It is quite shade tolerant - more so than many varieties of clematis - and it is evergreen to boot.

Here on Vancouver island the Layland Cypres is the most common hedge found and it actually does well if heavily pruned back 2x per year. If you go with this species remember that the majority of the growth hormones are gathered in the tips of the branchs over the winter months. By hitting them softly in the spring and hard in the fall with the hedge clippers you can have a lush healthy hedge within 3 years. Once the hedge is filled into shape reverse this so that you hit them hard in the spring and lightly in the fall. This will keep the hedge healthy and strong without requireing bi-monthly hedging.
Other choices for hedge plants that will do well in that ammount of space include: Holly, Pyrocanthus, and members of the ceder family. However all of these will require more constant pruning, about once every 6 weeks durring times of peak growth.

Leyland cypress is SO not a good idea for this situation! A 3' width is just not sufficient for a lot of hedging plants and especially Leylands. It takes a lot of maintenance to keep a plant that grows as fast and as wide as a Leyland to a very narrow profile and you need to make sure you have sufficient access. I'd also be concerned the aspect doesn't provide sufficient sunlight - while Leylands will tolerate some shade, they tend grow quite a bit sparser under these conditions. And they tend not to be very long-lived under many situations. Pruning these for hedging purposes is generally recommended at least 3 times a year (spring, summer and fall) and in the classic shape - narrow on top, wider at the base, sort of a lopped off A-line - to ensure the base gets sufficient light. I've seen some stunning Leyland hedges but they tend to be in rather open areas and the best looking are professionally maintained with very frequent attention. It's a lot of work.

Mobile home parks typically offer very small properties to landscape - space is tight. And with all the dark gloomy days this area receives for many months of the year, a big dark wall of high maintenance foliage would just be depressing. I'd also avoid any thorny plants as a hedge right along your drive, so nix the holly or pyracantha too.

An attractively designed screen or trellis graced with a few flowering vines sounds like the best option to me. It offers the narrowest solution, will be less intimidating in a small space and can provide both light and color.