Is there an official reg that states you cannot wear your uniform for public functions such as weddings, funerals, civilian court hearings?

Col (Join to see), in the Army there's AR 670-1, Wear and Appearance of Army Uniforms and Insignia. Paragraph 3-5 of AR 670-1 addresses wearing the uniform for public events. The Army distinguishes between weddings, funerals, etc., and public events (the subject of another thread here on RallyPoint). Paragraph 3-5 addresses wear of Army uniform at national, regional, and local events.

Weddings, funerals, and other public functions are addressed in various other paragraphs (for each uniform), where it says a particular uniform may or may not be worn. AR 670-1 says:

At social functions of a private or official nature, either before or after retreat, and while in transit to and from such functions. The male service/dress uniform is normally considered appropriate for social or official functions off the installation, such as memorial services, funerals, weddings, inaugurals, patriotic ceremonies, and similar functions.

I do believe it's service specific. Air Force would have its own regulation/rules. Here's a link to the Army regulation, if you're interested:

http://www.apd.army.mil/pdffiles/r670_1.pdf