The ward website administrator does not have access according to the access table for the information that you are looking for. I personally do not see why the ward website admin needs to see move in/move out, birthdays, and other private information. This is not part of the calling to administer this information. If you are using Google groups to send out information, I think that may be in violation of policy.
https://www.lds.org/help/support/meetin ... lang=eng#4
4.9 MLS Data and Membership Information
4.9.1 Information about members, donations, and financial transactions is confidential and must be protected from unauthorized disclosure.
4.9.2 MLS data, database tables, or schemas must not be used or shared to create or assist in the creation of third party software.
4.9.3 The use of MLS data and membership information in third party software is prohibited, whether obtained from within or outside of a meetinghouse.
4.9.4 The use of cloud-based services for storing and/or backing up MLS or any membership related data is prohibited.