It is likely that such an App doesn't exist. What you search for is an App that transforms your Smartphone (or Tablet) into an A2DP sink (that receives the Audio from a A2DP source).
If you're interested in building such an app or you might want to know why there isn't yet such an app, this question on stackoverflow might be interesting. There are several technical difficulties to build such an application but the most difficult one might be that android doesn't support the A2DP mode by simply not letting you configure its A2DP to be a sink.
Considering that probably much more experienced users/developers (no offense!) gave up this approach, it might be easier for you to get your WiFi working properly. There are several possibilities to fix a weak WiFi signal (adjust the antenna of AP and Client, removing obsticals etc.).