I may not be the best at anawering this but can only say from own experiance that the triad does not really work unless all three have a clear understanding and agreement about what each other want ansd expect.
Also in our experiance there must be a desire for the three of you to spend as much time together as possible, otherwise someone is always going to be left out. The fact that you and he have a family together is admirable but you must let go of the feeling of control, if you can accept that she has as much say as you and he does in deciding the things you are alluding to above then it may work. As for us we just all go together to events, people may wonder why but we dont care anymore.
Finally if you do not have ayearing in your heart to be with her she may not be the right one for you. Have you two gone out, off for a weekend together? There must be equal love and sexual energy all around or it is not a workable triad. Maybe you need to find another for yourself.