It's not completely about the dog. The story as I understand it is that they were going back to the apartment late at night and they came upon a stray dog. Kristy wanted to play with it because , well, she's Kristy and Kamila wanted to go back home. Kamila went without waiting for Kristy who took offense. They stopped talking for a day or two and Kamila cried.
There was an incident in Moscow too one time when the angels were spending the night. Kamila and Kristy had words in the kitchen and Kamila cried again, it was resolved very fast however. In fact I've seen Kamila cry three times, one time she seemed in physical pain but the two other times were over Kristy.