I don't know which way you were facing when you said "... to the right." So what area is that?

I'm a little lost in exactly what you are looking for. Are you looking for help with hardscape? .... planting? .... organization? ...?? It sounds like you think there were problems with the direction you were going originally. If that's the case, what are those problems? Please help explain what you need help for.

A thick mulch of coarse wood chips? You aren't going to grow any grass, and I can't think of any ground cover that could stand up to kids playing.

You have the start of a nice erosion problem along one side of the elevated area - fix that first, then worry about mud.

Yardvaark - Sorry for the confusion however, the area of concern is best shown in the first picture. Walking down the center steps you run into the dirt area on the lower section which runs width of the property. I'm looking for ideas on what others would do if they had this yard area. Landscape contractor was suppose to level and grade this area but I still had no idea what to do with it. The rest of the pictures were so people could see overall area.

Lazy_Gardens - Thick layer of mulch was one thought we had as well. The side eroding will have a dry river bed from the top down to the property line to channel water to the creek.

You already have the trees. It looks like it just needs a durable, low groundcover that can tolerate some foot traffic. Within it, you could strategically place large groups of daffodils, if those grow there. But they are not essential. I would only add shrubs along the property lines if there are things you need to screen next door.