Actually, Bishop Ukhtanes' history, which I reviewed here:http://www.orthodoxchristianity.net/forum/index.php/topic,16969.0.html
indicates that at the time of the split (early 600's) there was a sort of dependent relationship between the Armenians and the Georgians, to the extent that the Catholicos of the Georgians used to be ordained by the Catholicos of the Armenians. (page 41) I have no idea how that dependent relationship came to be, or how long things had been that way.
Bishop Ukhtanes' book is of value, because he basically just gathered together and organized the actual correspondence which was written by the parties at the time. One interesting thing is that the Catholicos of the Georgians, Kyrion, never explicitly states why he is breaking away. The thing that started the whole business was Kyrion's ordination of a Nestorian bishop, an ethnic Khujik, named Kis. (page 42.) When confronted by the Armenians about this, Kyrion at first skirts the issue, but then finally writes a letter confessing the "four councils" of the Greeks (not five, surprisingly) and says "I shall pass through Armenia only if I have to, on my way across; otherwise I have no business to be there." (page 101.) Ouch.
Bishop Ukhtanes guesses at why Kyrion would do this, and relates an oral tradition which until that time had not been written down. He tells a story of when the Armenian Catholicos invited Kyrion and another Catholicos to dine with him. The Armenian Catholicos served the two men with his own hands, but served the other Catholicos first, because he was elderly. Kyrion was insulted by this and became angry over this, saying he should have been served first, since he had more bishops than the other, elderly, Catholicos. The Armenian Catholicos tried explaining to Kyrion that it was proper to serve the oldest first, but Kyrion remained angry and left the table. (page 120)
Who knows if that story was true. Bishop Ukhtanes himself was not really sure about what really motivated Kyrion. A desire to be independent of the Armenians was undoubtedly at least part of the reason, as Fr. Peter said.