Let's get the elephant in the room out of the way: Chloe Chrisley looks different from all of the other folks in the Chrisley family. That's because she's biracial, half Black and half white, whereas the rest of the Chrisleys are all thoroughly Caucasian. The daughter of Todd's eldest son, Kyle, and Amber Johnson, Chloe is a grandchild of Todd and Julie, which is why she appears on the show Chrisley Knows Best alongside them.
If you're not familiar with Kyle's story, or why he stopped being on the show after the first season, you should know it's been a bit of a rough road. For one, according to E! News, Kyle has struggled with bipolar disorder, and, at certain points, he has reportedly refused to take the medication he needs to be healthy. He's also had problems with substance abuse, something he admitted on his Facebook page, which has hampered his parenting ability.
As for Chloe's mother, she has had brushes with the law, as she was reportedly arrested and charged with Medicaid fraud, as noted by Starcasm.