If the DA does not offer an open file policy you'll have to file a discovery motion for the information they have. The DA has an obligation to produce exculpatory evidence but you do have the right to review their evidence. Dallas county at times will require a motion to be filed before they open their file.
As to your appointed attorney, if you aren't satisfied you can always hire your own attorney. It might seem expensive but it will be worth it in the long run.
And yes if you give your attorney permission to speak with a family member about your case, they can, BUT you run the risk of waiving your attorney-client privilege on certain communications, Which is a very important privilege to maintain.
At the end of the day, it's your freedom on the line and you need to be confident with your attorney.