"She is fine and naughty," Kelly's mom Sharon, 60, joked Monday on The Talk. "After the show, I'm going to go and pick her up, give her a good smack."
Sharon says there's even a silver lining in the fact that Kelly was at work during the attack.
"We were very blessed that ... when she had her seizure, she had it while she was filming, so it was filmed," says Sharon. "We needed that to show the neurologist so they could see what was happening."
Added the Osbourne matriarch: "Kelly has asked me to thank everybody who sends their love to her and have reached out to her. ... We all believe in the power of positive thinking and sending good vibes. We strongly believe in it in the Osbournes and we want to thank everyone. And I thank her doctors and I thank everyone at [Cedars-Sinai]."
A rep for E!'s Fashion Police co-host, 28, issued a statement to PEOPLE on Monday saying that Osbourne is still in the hospital "as a precautionary measure."
"She is in good spirits and looking forward to getting back to her busy schedule," says the rep.
Reporting by JULIE JORDAN