The information you gave concerning Lay Associations may be a bit confusing to some.
There is a distinction between an association, ie: Sodality, Knights of Columbus, Marian Helpers, Apostles of Divine Mercy etc.and Third Orders. It is true that one may belong to as many Associations as they like but a person may belong to only one (1) Religious Order. Third Order members are actually members of a Religious Order.
For instance, I am a Third Order Carmelite. I may not belong to any other Religious Order, just the same as a Jesuit may not also be a Dominican. A Diocesan Priest may belong to a Third Order if he should choose to, and many do.
I may belong to an Association with permission of my Director, providing it does not interfere with my duties as a Carmelite.
As for wearing a scapular in private. Unless it is specifically prohibited by your Director or Prior you are usually allowed to wear what you would like in your private prayer. I wear a cincture to remind me that I am a slave of Mary and Jesus.
I hope this helps clear things up.