"Nothing more adorable than a big brother reading to his little sister," Clarkson, 35, captioned the sweet Instagram snap.
The American Idol alum posted another picture over the weekend of River Rose during nap time.
"Snoring and all, she's the coolest girl I've ever known," the proud mama wrote.
Clarkson, who is also stepmother to Blackstock's daughter, Savannah, and has a 1-year-old son, Remington, was recently tapped to serve as a coach alongside Adam Levine and Blake Shelton on season 14 of The Voice, airing in the spring of 2018.
"I'm so excited to join The Voice at NBC," Clarkson said in a press release. “We've gone back and forth about a role as a coach for years, but the timing hasn't been right until now. I have always loved appearing on the show as an adviser or performer and established an amazing relationship with the network during my Christmas special. I can't wait to turn my chair and see the faces of up-and-coming artists and provide them with the help and support they’ve needed to break into the industry. Watch out Shelton, I'm comin' to win!!"