My non-observant family wants my family to come watch the 4th of July parade with them. This is during the 3 weeks however and I’m sure there will be live music in the parade. What should I do? They will most likely be very offended if we decline.
Under extenuating circumstances (if they will be offended, as you write, and they won’t understand the reasons for your declining the offer) there is some room for leniency.
Yet, it is certainly correct to avoid this if possible.
If you go, you should be careful to avoid actually joining in the festivities, and only to watch from afar.
The customary prohibition against music in the Three Weeks is in fact a prohibition against dancing, which is mentioned by the Magen Avraham (551:10). This is extended to music by later authorities.
Although a parade is something that involves happiness, it is nonetheless distinct from the concept of dance that the Magen Avraham refers to, since it involves viewing rather than participating.
Yet, the custom is to avoid joyful music as well as dancing, and it is possible that the parade itself, as a joyful and extravagant event, is more stringent even than regular music. Thus, if you must participate, you should do so from afar, and certainly avoid actually taking part in the festivities.