Honestly, your talking two different items of equipment here. So lets try this, each Dlink device has a certain sweet spot for broadcast the WiFi radio signal. Each one starts to drop off signal and range when you get farther way from the source. Trying to relay and bridge the source signal, the device that is trying to relay, extend or bridge the source signal is having to maintain this signal and probably by design, is going to degrade the signal only if it's getting a bad signal or the noise and interferrence is bad due to the distance considerations. If your placing the relay device towards the farthest way from the sources farthest signal range, then the relaying device will probably not get the best signal it should be getting and it will probably fail to provide the continued and relayed signal that your hoping for. So you need to probably place the DAP closer to the source signal to ensure your getting the best signal into the DAP so it can relay and rebroadcast a good signal down the line. If the DAP is not getting a good signal, then what we used to say in the military, Garbage in, Garbage out.
What kind of streaming are you trying to do? Full on 1080p BluRay or just DVD or internet, or netflix?
I did some testing yesterday. This is a limitation of my Boxee however I did try to stream Blu-ray content from my server over 2.4Ghz N only and the Boxee would keep re-buffering. I hoped that single mode N at 2.4Ghz would be enough, it's not. Unfortunately the Boxee only supports 2.4Ghz wireless so I can't test to see if 5Ghz would work. However streaming from Netflix and other sources worked very well and the boxee didn't re-buffer during non blu-ray movies. I have a DGL-4500 set up as and AP connected to a DIR-825. The limitation of the Boxee to be able to do 5Ghz and the large amount of data in the BD files is to much for 2.4Ghz however other Internet streaming and netflix was very good for 2.4Ghz and boxee.
I would recommend that you give 2.4Ghz a try first and see if what your needs are will be satisfied by 2.4Ghz instead of 5Ghz. Not all streaming needs 5Ghz. The range on 2.4Ghz might help with your distance and may get you better range between the DAP and DIR. Or you need to move the DAP closer to the DIR to maintain that sweet spot.
Honestly, i do prefer using wired over wireless. I do understand that not everyone can do that and it's not feasible. Just wired can handle so much more then wireless.