The phrase often implies a power imbalance where one person controls another. At work, I feel I always have to dance to my boss's tune.
Pro Tip 2/3
Negative Connotation
Using the phrase can imply a lack of freedom or autonomy which is generally seen negatively. He doesn't just dance to his wife's tune; he actually agrees with her.
Pro Tip 3/3
Resistant Variations
Saying someone 'won't dance to someone's tune' shows resistance or independence. She won't simply dance to the company's tune; she intends to negotiate.