There is no confirmation which would suggest this, so take it as my "sleuthing" intuition: I think in the beginning, before Caylee was found, the Anthony's kept in contact with JB. I think they attempted to get JB to follow THEIR demands and JB had to be forceful and point out that Casey was his client, not them. I think that's when we first learned that the Anthony's did not like JB.
Once JB set himself up as adversarial to the Anthony Way, I believe was when they first lawyered up with MN. They learned that a Casey Defense could very well include an Anthony Attack. There was a flurry of "we believe in our daughter, she didn't kill Caylee." "Caylee is alive, Casey is innocent." comments. Their stand behind their daughter did not include any visits. Once people started speculating on that, the reasons given were that they didn't want their visits to hit the airwaves "the next day like the other ones" which is a false presentation of what happened, since it was months before we saw the jail videos. In any case, the Anthony's are now separated from Casey, and Cindy and Casey begin their twice-removed jockeying for control through their lawyers. For what it's worth, MN tried. Really really tried to get the Anthony's (Cindy) to pull back, quit the drama. As we can see now, once MB and the PI's got involved, MN quit on November 20, siting that he could not continue with the Anthony's and that he would not help defend Casey.
I do not know precisely when Conway came onto the scene, other than the announcement the day Caylee's remains were found. It seems now however, some of the statements he is making about it being "his" tape would lead me to believe he interjected himself a lot earlier and we only heard about him the day the Anthony's returned home from their West Coast Tour. In any case, we can be sure that by this time, the Anthony's have to feel that they need to do something to prevent Casey from throwing them under the bus, and all of a sudden we're hearing the word "immunity" being used more frequently than a box of tissues in a room full of flu sufferers. There is "something" there. I don't know what, but this board is full of speculation as to what it could be. Then Lee hooks up with the genius, T Luca, who should be fired for incompetence (but that's just me). I'm pretty sure that Luca and Conway have chats, though it would seem their interests are going to separate fairly quickly if they haven't yet. I doubt that Baez wants Luca within 10 feet of him.
So, to sum up, the interests of each of the Anthony's is served by attorneys and those attorneys are charged with protecting their clients' interests. It serves them well to keep them separated. George and Cindy can have Conway because of husband/wife privilege. But I wouldn't bet on either one of them sticking to that if their own interests would be better served by tossing the other one under that bus which seems to have been circling for a drive by for quite some time.