Just to add my little piece..i recently started a training group with my instructor's permission where i live...and my gf, who trained before in a different style, comes with me to help me get these guys started. Honestly, I really appreciate her being there and I haven't noticed any weird vibes about her presence. In fact, in the car on the way home after practice, I take the opportunity to ask her about her honest opinion about class...and even about how i did! haha So if both of your intentions during class is to train...I couldn't see any reason why it would matter that you are a couple outside of the dojo.
Jeremy