If the moisture is in the corner then you are better off digging up both walls to make sure you have the corner covered. From the previous post I take it that the foundation in a block foundation. Block foundations are notorious for cracking in a Christmas tree pattern in the corners due to excess pressure.
I would dig up both walls by hand approx 12-24" deep and approx 12-20" wide pitching the bottom of both squared bottom trenches to the corner. Clean the walls with flat shovel then wire brush and let dry. Use a plyable ( if too stiff then last the 5gal bucket sit in sun ) roofing tar to coat the walls, apply the 4-6mil visqeen to the wall and let it sit in the trench like a gutter running parallel with the wall.
Install at least 3" corrugated perforated pipe and covering with 1" washed round gravel. Do not use pea gravel as it will clog with sediment very quickly. I personally would run both pipes to the corner and tie them into the d'oh spout line. If it is deep enough and you have enough fall away from the home. If it is not deep enough then you would need to take it deeper as long as you have enough fall away front he home.
The corner can get tricky with the tar and plastic because you don't want a gap in the two " systems " you would want to have a Seperate layer of tar and plastic over the corner BEFORE you bring your two systems to the corner for a added layer of protection and then try to wrap the system from the deepest wall ( behind the raised planter area ) AROUND the corner and then tie them both not the d'oh spout line and away form the house. Once the gravel is in both trenches cut some more plastic the width of the trench and put slices in it with a razor knife and then install over gravel before dirt backfill as a filter to keep soil from settling into the gravel over time.
You may have to remove some of the block retaining wall to accomplish all of is but it should go back fairly easy. Just remember to have nothing but gravel under it so the wall won't settle.
I have waterproofed hundreds of basements and worked for the nations largest basement waterproofing company ( EVER-DRY ) and this is the way they would do it. It sounds like a lot of work but it really isn't. Could be accomplished in a long weekend say labor day weekend coming up. I would do the digging by hand. If you hit the gas service with a mini excavator then you have a gas leak, weekend charges from the utility company to repair and that could cost easily $300-$600. Also, call you local or state utility locating company to locate and mark all utilities which SHOULD only be your house electric, telephone, catv and gas service.
If I were giving a estimate on this outside work I would figure 1 1/2 tons of 1" washed gravel, pipe, plastic and tar. Approx $200-$300 for material.
Another aspect is if the moisture stains on the interior wall are low to the floor then you MIGHT need or want a sump pump in that corner to evacuate water table water under the floor. If possible put it right in that corner below the floor line about 12-18" and run the discharge out the wall and tie into the downspout line to get water away from home and prevent it from recirculating.
This is a lot of info and quite a bit of work but if you continue to let the problem go then the foundation will continue to get weak from the water pressure especially if it is a block foundation.
If I were closer I would come by and help but feel free to pm me and we could exchange #'s for more clear direction.
Good luck to you and I hope I have helped.
