Having led the Shu family to their current standing, the patriarch of the Shu family was no fool. He knew that the most important thing now was to convince the Mu family to agree to a ceasefire. Otherwise, if something major happened before the Crown Prince's conferment ceremony, the Mu family might be fine because they're in-laws with the royal family, but the Shu family would not be in a good situation.
The Emperor didn't like aristocratic families to begin with. Even a first-class aristocratic family like the Cui family had to avoid them, let alone a third-class aristocratic family like the Shu family.