Each rhinoplasty should be individualized for each patient. In almost all cases, the bottom of the nose is too wide if it is wider than the distance between the inside corners of the eyes. In most cases, narrowing a wide tip will improve the balance and harmony of the face. However, the amount the alar bases can be narrowed depends on the configuration of the junction of the nostril rims with the upper lip. If the nostril rim curves inward to meet the lip, the patient is a good candidate. However, if the rim at this location is straight and meets the upper lip at a right angle, it is very difficult to narrow these noses and keep them natural looking.
As far as your nose widening when you smile, this is normal in most noses. the smile muscles travel from the cheek bone and the nostrils. When these muscles contract, they pull the nostril bases toward the cheek making the tip wider. This is made better by projecting the nasal tip forward so there is more tension at this junction of the tip and eyes which resists the natural tendencies for the nostrils to move laterally.