I know the subject title is a little weird, but that is the only way I can describe a couple areas in my yard.

The front of the house faces east so I get some morning sun. The neighbor across the street has a large maple that blocks some of it and I have a huge (120ft) pin oak right out by the street as well, but it is on the north edge of my property and is limbed up high enough that it does not really affect the morning sun. Where it gets interesting is the area underneath the oak is obviously in shade most of the day, but then it gets about 2-3 hours of intense afternoon sun and I cannot figure out what to plant there at all. I have almost the exact same scenario in the back yard. The yard is wooded but the utility company came through this past summer and took down 16 small trees plus limbed up several of our larger trees creating the same shade most of the day but intense afternoon sun for a few hours along our back fence. Any suggestions on plants that can handle some filtered sun/shade for a majority of the day but handle the intense rays of the hot afternoon sun for a few hours?
Existing Hostas have seemed to burn, I tried some coneflowers but they are alive but are very weak and only threw up a few flowers. Some Hydrangeas were existing have lived, but again, no real flowering in the 2 years I have lived here and need lots of water almost daily to keep them looking good. They are on my list to transplant to someplace a little less harsh.

Sorry for the long description and rant, but I am at a loss of what could work in these areas.