I am a diamond member myself and I have this option, although I'm pretty sure it's available to non-premium members as well.
Go to your game (should have a chess.com/echess/game url) and go to the position which you would like to play it out from (using the arrows to go from move to move). From there, click the Analyze button below the arrows.
To switch board side, click the Moves tab, to the right of the Message tabs which you'll be on automatically. Then click Flip Board on the right side, below Get PGN.
Hope I have been at least some assistance, and enjoy your time here! 
Hi - New to this site, but very much enjoying myself. Apologies if I didn't look hard enough, but is there a section on the site for FAQs?
Specifically, I'd like to know if it is possible to take a position from a completed game and play it again from there. Further, is it possible to do the same but switch sides? Or is this an option available only to premium customers? (Haven't paid yet, but will most likely do so shortly.)
Any info would be appreciated. Thanks in advance.