After she left the show, Kelly said something to the effect that they hadn't been real members of the ALDC since the show started... which would mean something to the effect that they stopped signing Abby's studio contract before the show began, and didn't start signing it again even when they were cast for Dance Moms. Abby had sort of said something vaguely similar at events when they were filming Season 3.
Now they did train at Abby's for the show after they were cast, etc. They also did ALDC events and competitions outside the show during like the first season, and part of the second season.
And Kelly Hyland hit Abby Lee Miller's bumpit and was arrested.
When it comes to leaving the show, Abby seemed to be putting pressure on the Hylands to sign her studio contract (which is different from the contract they signed with Dance Moms producers), and also pressuring them to spend more time in dance training, generally with the "everyone's replaceable" threat.
On the weekend where the Hylands weren't at Nuvo with the rest of the ALDC early in Season 4, Abby played a trick on them, by having Maddie and Kalani do a duet by surprise against Chloe and Paige at a different competition (unlike Nuvo, an easier one that was really produced just for the show). Later that day, Abby also gave Brooke a hard time in the dressing room. Kelly got really upset, and Abby and Kelly got into a physical fight (I assume you saw that, it's the really big final fight they had.) Abby called the police, and went along with pressing charges I guess, and there was a legal restraining order by a judge so they couldn't be around each other. So Paige and Brooke couldn't be near Abby anymore (except without Kelly), even if they wanted... and I'm not sure they wanted to be with Abby even with Kelly around, by that time.
Then Abby and Kelly couldn't or wouldn't try to settle their problems with each other, and kept fighting each other through the courts and media; and then Kelly also burned her bridges to ever coming back by also suing the show's producers. So that's how things "ended."