The dancer was later spotted at dinner with brother Val Chmerkovskiy and their parents.
"There's a big chemistry issue," a source told People of Chmerkovskiy and Lachey. "They both have big personalities and that's not always the best recipe for a good partnership."
"They've been fighting a lot," the insider added.
Lachey said Tuesday in an interview with Us Weekly that she appreciates Chmerkovskiy's training, but confessed she often keeps quiet in rehearsals.
"I just know that when I'm on set he's my coach and I'm the student, so I listen a lot more and I don't speak up as much because this is a field I don't know," the television personality said. "He's trained me and taught me so many amazing, wonderful new things."
"But at home I think I'm a lot more outspoken!" she added.
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