It hadn't - the girls were selected for the show. Prior to the show, Brooke and Paige danced in different teams, as did Maddie and Mackenzie (for instance.)
You see a very specific type of dance all the girls do - lyrical/contemporary/jazz usually, but the girls all took ballet, tap, lyrical, hip-hop - so had different teachers. Abby was the director of the company along with her mother, but the girls had very little to do with Abby herself, I believe. I think Maddie and Mackenzie knew her better as Melissa worked at the studio.
There was clearly bad blood between Kelly and Abby. Sometimes I was definitely on Abby's side. Other times I hated what she said about Brooke and I thought Abby was bitter about Kelly having married well - there were a few barbs about Kelly having done nothing with her life other than work on the Clinique counter.
I didn't like Christie at all in season 1. She came across as jealous and hostile and the girls were so young then it did really affect them. As the series went on, Christie really grew on me. I think for Christie it was a combination of having a naturally combative personality - she was raised in a very difficult home, I know, and - deducing here - I think to surivive, she had to fight. Chloe was always so meek and gentle she did it 'for' her. I think Chloe is more gregarious than was let on, or portrayed in the series anyway! Christie did have a very soft side to her. She showed real compassion to Abby when the dog died and she really backed Chloe up. I admired her for that.
Abby is a bizarre creature! But I do think she was never emotionally stable. She was talking to the girls about her dad's death once and was crying in front of them. I think she has very little support: no partner and possibly no real friends. I'm not sure. I also suspect she would have liked a child or children. She seemed to love and resent the girls at the same time.