Can a prosecutor offer a plea deal even though the victim family is against it?

Yes. They are supposed to get the victims approval but they never do so they can just close the case out. I was a victim and I was told that they were going to see about a deal. They told me that I'd have to approve to the deal before anything. The DA then didn't send me notices of the hearings. They left him off with 1 year probation. I raised questions after and they said that it was up to the DA and not me. They said that it's just a courtesy to ask the victim not the law. Sorry!