It's sad that the father doesn't want them to participate, but that said, I think it depends on 'in what capacity'....
.... I went to a wedding where the children were included, but in an utterly horrible way. They were invited on the stage for a sort of family ceremony where they were admonished by the pastor to promise to honor and be obedient to their new stepmom (our friend). It was fairly upsetting for the kids (they were crying and felt embarrassed) to say the least. So, if I were the father, I'd agree to participating as long as the ceremony was not going to involve the kids making a commitment, as they didn't choose the new parent they were getting.
Sorry if that doesn't make sense.... it just left many of us guests horrified, so I can understand the reasons a parent might be apprehensive.
ETA: per your SWH, I would say that their participation would be a lovely thing. I hope the father can find a way to feel better about the changes in their lives. Was there an affair between the mom and the to-be husband while they were married? I could understand some bitterness in that regard, but even then, hopefully, Dad could come to see that being agreeable to this is still the best route.