Well you hit on a key item. The plants in the pot with potting soil do better than being directly in your current soil.

So you just need to amend the soil. Generally, that will be just adding compost to your yard soil, but you can do more different things also, such as measuring your soil PH conditions, etc

For adding the compost part, it is sometimes recommended that you can just add it on top, but in your case, since you don't have other plant growth there that you want to keep and you are interested to do some digging anyway, you can till it into the top 3-4" of your soil (a little deeper also if you want to plant plants with deeper roots)

However, I'd suggest to do that this year and go with some casual plants that you don't mind if they die. If this works and your soil can sustain them, then next year, you can try other more permanent plants or perennials.

The other part is to ask if this area is really right up against your house, is it getting any bad water from gutters or lack of sunshine from the house blocking the area?

Rock gardens or xeriscaping is also becoming more popular, especially with the water restrictions that many homeowners are facing. If you're willing to redo the landscape for that, it's a viable possibility also.