Upgrade to Internal Build 7.1.5202 or later.
In the build is added support for creating related data fields working with default source (provider) per site in multisite environment. In other words, the field will now automatically resolve which is the default provider for the current site, and allow you to select items from it.
Internal Build 7.1.5202 release notes: http://www.sitefinity.com/developer-network/forums/general-discussions-/internal-hotfix-builds#xtd_1FCk-UaMwcC3XrrPuw
Important: The Internal Build 7.1.5202 or later, provides a fix for any newly created related data fields, so if the use case allows it, we recommend to proceed by recreating the existing fields. If recreating is not possible, please, follow the Workaround in the article.