I know this is an old post and seem to remember a newer one, but couldn't find it. I wish you could limit the forum search to just search the topic titles, but anyway....
I was thinking about this recently and realized why this worked so well for us. In our case, it turned out the Mrs enjoyed seeing me have fun as much as I enjoyed seeing her have fun.
I also realize that "convince" is not really a great word here and perhaps "accept" may be a better word, but regardless of the word, IMHO it is much easier to get into swinging when BOTH partners enjoy seeing (or at least the idea of) the other having fun with others. Put differently, I think it would be more difficult if one partnerf was not into the idea of their partner playing with others.
In our case, the biggest obstacle early on the Mrs had with being a hotwife type is wrapping her head around the idea that I could actually enjoy seeing her fuck other men. When she realized she herself enjoyed seeing me have fun, it was much easier for her to understand how I could feel the same way about her.
This isn't to say that this is the only way this could work, but it certainly made it easier for us to get into the LS. That, and realizing back then that our new hobby was really just recreational sex.

