The bride's cousin has Asperger's. I don't know how many of you realise the implications of this, and how hard it would nave been for him to start singing in the middle of a room full of strangers. It is possible that he was not announced "officially", because he probably had been amping himself up in order to dare to sing, and having Asperger's, and hence lacking in social and etiquette skills, he probably just started playing and singing when he felt he dared to. You know, when you are in the autism spectrum the mere idea of asking people to listen to you, or "announce yourself", can be terrifying.
The bride was probably amazed and touched that her cousin was being brave enough to sing and play in front of strangers for her. She was probably so proud of her cousin, and wanted everyone to listen to him. That is probably why she was frustrated that a number of guests, among them your DH, kept talking and laughing loudly.
As people who have contact with someone with Asperger's know, her cousin could be easily upset by these people talking and laughing and it could have meant he would freak out, stop singing and playing, and have a breakdown. This would have been really sad considering the effort he was making. And would have ruined the beautiful, magical moment he was gifting the bride with, besides crushing his confidence.
So the bride decided to go to the noisy party (i.e. your DH) and ask them to stop talking, as briskly as she could. Because honestly, her cousin dedicating that song to her was probably 100 times more important than your DH having a laugh at that very moment. Your DH not having Asperger's, he would have the chance to go back to the person he was talking to and just go on laughing any other time. But her cousin would more than probably only have that shot at the song. Your DH should have been the big person here and realise that his being told to hush was a tiny inconvenience compared to the bride's cousin having the chance to perform.
You were very unreasonable to get offended by being told to hush, and even more unreasonable to "threaten to leave". Once the bride explained, you should have understood and apologised yourself. Then everything would have been ok and everyone would have enjoyed the ceremony. But no, you CHOSE to take offence at having to shut up to let a person with Asperger's sing to her cousin, and now just can't let it go and are going to turn it into a long-term fall-out with your supposed "friend".
You should be ashamed of yourselves. Honestly, you didn't deserve to be there.