Can one attend a wedding on the 12th Jamadi-ul-Awwal? If not then how can one explain to them,that it is the martyrdom of Lady Fatima Zahra (as) on the 13th Jamadi-ul-Awwal.

It depends on what date you observe the shahadat of the lady of light. If this date you observe as her wafat then you should not attend and they need to respect your religious sensitivities.