Call me old-fashioned but, to me, it reeks of 'emotional affair'.

You both still have feelings for one another but won't leave your respective marriages, yet intend to continue seeing one another?! Ouch. Your wife kinda feels like second best. No wonder she has issues with your ongoing relationship with that other woman. Frankly, I don't know who wouldn't have an issue with that.

How would you feel if your wife was in love with someone else, knowing they were also in love with her, and she was still seeing them right in front of your nose? Would you be okay with that?