How can we repair out stucco cinder block wall?

Sadly the developer of your area used cinder block and not slumpstone. I would ditch the stucco and just paint the cinder block the same as your house and call it a day. Or if you are adventurous, get a muralist to come in and paint a scene on it for you, which could be way cool and a conversation piece. I have seen several done (but done well), and they add to the feel of the yard and a pleasant attraction rather than a sad blank wall.

Can you switch to artificial wood fencing with a support system behind it, or plant something inside the top holes of the cinder blocks (bamboo, prairie grass, cactus)? You might be able to attch lattice against the cinder block, and grow vining vegetation. Your watering capabilities are probably rationed, so perhaps trailing Lantana is an option? Do you want to block out your neighbor's yard height? You're right. $5K is far too much to have to spend, repeatedly, when a long lasting alternative might exist.

Plant vines to grow over and cover it

https://hotgardens.net/vines-and-climbing-plants/

Hey Nana was the cinder block wall prepared before putting on stucco? Here's what I mean-what you are doing is basically putting cement to cement and that will not stick. If you do an acid wash on the block it opens up like small pores so when the stucco is applied it actually goes into the block. After putting on stucco before painting waterproof it (several coats). Then use elastomeric paint mixed with SEALCRETE. Seal Crete is waterproofer. Another way is to put on the outside of house the wire screen before putting stucco on. Some people use the screen inside their home if they are replastering their walls. Please get a hold of your city or county building dept and have them check on the water that keeps coming your way from your neighbor because they built up their property. Your neighbor might be responsible for having to put in some type of drain to keep this from happening. I know this is a lot but I hope this has helped.

Acid can be Muratic acid that used for pools.

We had that problem too. We live on an island and the one house we built was in a lower area where we would get flooded at times. We ended up having it all scraped off and put stone around the whole foundation. Problem solved. The cost was quite a bit but in the end, we didn't have anymore problems and were not putting money out each year for repairs. Painting was a problem, too because it peeled like the stucco.

And stay away from vines next to your house, they are very destructive, digging their roots into your house and compromising the structure.

Installing artificial wood products on the inside wall may be a great solution! Using wood here isn't recommended as it rots. I have lantana that works well in one area only-- unfortunately, areas with our full summer sun usually do best with just palms & cacti. 🙄 Thank you!

Before you redo the wall, have a French Drain put behind the wall where the water is coming from.

Have you gone to the original contractor? And I would just inquire from city or county if this would be part of inspection for the original contractor. Maybe a deal could be worked out between you and original contractor. St least it won't hurt to try.