I totally agree with your daughter's reaction. She has seen your DH choose a path that effectively says a big "screw you all" to you and the DCs.
She saw her dad make selfish decisions that have devastated the world she lives in, and he knowingly did this. Why would she forgive him?
If he as in addition to this, broken a specific promise to her, then I think she is beyond reasonable that all she is doing is ignoring him rather than telling the two of you exactly what she thinks of you both.
You DHs behaviour now is asking a 12 year old, who will know and understand far more about what has gone on than either of you realise, to just shut up and forget it ever happened and treat him like the alpha male, in control of the household, all powerful dad that he thinks he is.
You DD's reaction is a reasonable, proportionate response to the situation, and one any other adult would be allowed to carry out without being told they must speak to someone who just willingly tore apart their world, and that of everyone they hold dear.
Does your DH realise it could be years, decades or never that his 12 year old daughter decides to forgive him for choosing to throw away his family for sex and a OW that clearly didn't mean much given its already ended.
I would behave like your daughter has, and then some, and I would not change because my mother asked me to. She has been terribly wronged and you are asking her to forgive and forget immediately, just because you feel you are ready to. If you force this, you risk your relationship with your daughter. At the moment at least part of her reaction will be out of protection of and loyalty to you, her mother. That is a valid feeling.
You should both have more respect for your daughter and your DH needs to give your daughter consistent solid reasons to respect him. At the moment, she has none.