I was also thibking about thise things. if i were to hire, which would be cheaper?

French drain most likely will be cheaper than a retaining wall.

Since it isn't obvious what the issue is, why anything needs to be done, where the water is, where the water should be, why not just do all of the above? How about adding a waterfall, while you are at it, or a miniature version of the Great Lakes?

So long as the lawn next to the house is graded away from the house, it doesn't matter a great deal what happens further out. Since we have no idea where the house is, or what the grade near the house looks like, there isn't much useful to be said.

I agree. If it's not causing a problem with water running into the house, just work with the slope. In the picture you show, a groundcover for shade--Geranium macrorrhizum, Big Root Geranium--would look great.

Natalie: has water entered your patio or house when it rains? Does the slope of the yard go down all the way to the house? If so, you need to make a path for the water to run off away from the house. That is where a French Drain would be of help.

I think you are over thinking the situation. From looking at the picture, it appears the ground behind the shed (on picture's left) is no high and even possibly lower than the ledge the shed sits on. There for the amount of water coming down the slope into your yard is just from the shed platform and the small slope. Further it looks like the natural channel runs parallel to the long side of the shed, across the yard from the near neighbors yard to the far neighbors yard.

If this is a correct analysis of the situation and there is not a dam holding back 1000's of gallon above your yard, the reestablishment of the grade down the hill should take care of all of your water problems.

It looks like the play may have created a slight dam across the channel, preventing water from quickly moving through your yard and diverting the water possibly toward the house.

Again if I have analyzed the situation. a couple of hours with a shovel would correct the problem. Personally, I find the best time to work on water problems is when you have material to work with. Thus the poncho and shovel working the area in a rain storm.

While it will be difficult with the children playing in the area the reestablishment of grass would help any erosion problems you may have. With children grass can come when they grow up.