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.
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"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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