This is how I would deal with it too, although I think you need to understand how your dd is feeling. If she is scared to be in the same house as him alone, then that puts a different slant on it and he would need to be seriously remorseful for his actions, and DD to be fully on board with him staying in the house.
Sibling abuse is very real and rarely taken seriously, as many posters on here have expressed their lives and relationships with their family have suffered because of abuse not being taken seriously.
It sounds like there is something going on with your son, and I do think you and your DH need to get to the bottom of it, saying it's all sorted is not acceptable and he needs to understand there are very real consequences for assaulting someone.
As a pp showed when turned to involve a husband and his wife everyone would be taking this a lot more seriously, my personality would allow me to offer the person a second chance, my DH has never been violent in any way to me, if this scenario occurred it would be so out of character I would give him the chance to rectify with a heartfelt apology and the promise that any signs of subsequent violence would without discussion be the end of our marriage, the remorse would be the first step though, if there was no remorse there would be no second chance.
I understand posters saying kick him out, but I do think if DD is ok with it, then it could be resolved without resorting to that, but she has to be the lead on this, her safety matters more than his feelings.