He probably doesn't know how to act, and feels awkward about holding her hand and showing affection to her in front of you the way he normally would, and wouldn't want to ignore either of you.
What's the hurry? Why can't you just give it more time? My spouse has been in another relationship for over a year, and we still haven't all hung out together. Although, i am not really interested in that because i have other things i'd rather do with that time.