All the main characters have hard lives involving under appreciation from their friends and families, this facet is pretty emotional.
One character is doing driving time trials to be the gang's getaway driver. When he is annoyed to drive seriously fast to his father's stern urging, there are a few seconds at the end when he's momentarily alarmed that he accidentally ran over his father. However, the father swiftly emerges from the side perfectly safe and pleased at the speed his son achieved.
Ash finds out that her boyfriend had been cheating on her and breaks down emotionally in one scene (not violent or graphic at all, just a little sad).
Mike the mouse is put in danger after getting into debt with some gangster bears (He's the Goldilocks to the three bad bears!), this adds tension to the movie.
Buster loses literally everything at one point, causing him to become dispondent. This is pretty emotional.