You have the choice to go to the wedding or to not go to the wedding. It is not required to observe days of mourning for days of wafat or shahadat (death/martyrdom), it is only recommended. Weddings are also optional.
In my view, if you have a good relationship with your family, or if you will regret missing the wedding, then you should go. Allah knows that your intention in your heart is not to disrespect the Prophet (S) and to maintain family ties, and maintaining family ties is also good. The Prophet (S) was compassionate and merciful and would be unlikely to criticise you for this!
However, you also have the choice not to go, and it isn't necessary to go.
This is as long as it doesn't involve disrespect to the religion. Most Muslims don't know that the 28th Safar is the death anniversary of the Prophet (S), and don't commemorate this, so they aren't intentionally being disrespectful when they schedule a wedding. However, for instance, if someone schedules a wedding on Ashura, and they know some Muslims commemorate Ashura, then maybe attending the wedding would convey disrespect to Ashura or give them the idea that you don't take your faith seriously.
The biggest emphasis in our tradition is on avoiding celebrations on Ashura. It is also good to avoid celebrations on other sad days, but the biggest emphasis is on Ashura.
There are a lot of shahadat/wafat days that are commemorated, so, sometimes, in an environment where not everyone shares the same religious traditions, it can be difficult to observe all of them!