I saw all the fuss here before I had a chance to watch the service online and I have to say...is that all there was?
I saw a four year old behave very well for her age for a very long time. Until she didn't, but even then, it was within the realm of normal misbehavior for a child of her age and addressed pretty quickly by her parents. Chris tried an approach that didn't work at first, trying to silently get her attention to tell her to come back to her seat (doesn't work if the child doesn't look your way!), but once he realized there was no alternative to getting out of his seat and adding to the distraction he scooped her up and handed her off to family on the pew behind.
Madeleine did laugh about the way Leonore circled around her at the end, but given that things were basically over and this was, as people have pointed out, the kind of service that is meant to be a celebration where children are welcome to be children and not one that is meant to be sober and solemn, that didn't seem problematic to me. When Leonore rolled on the floor, on the other hand, nobody laughed it off or ignored it; Madeleine had her hands busy with a fussing baby but was clearly seen whispering at Chris to take care of things...which he did. As for the photos where she's behind people, it looked from the last couple of pictures in the shoot that the adults were surprised to realize she was doing it and probably hadn't even realized during the first few shots. And once they did realize, they decided they were finished rather than let her keep doing it.
They're in a very tough position. She's quite spirited, so it's going to take her a little longer to learn how to be restrained at these sorts of events. She's still at the age where it is developmentally normal for a tantrum to sometimes follow correction. There is surely nothing they want to avoid more than a public tantrum on camera. It's one thing to have video clips circulating of your kid being a happy (if inappropriate for the occasion) kid, it's another to have video clips of your kid being angry and/or loud. But bottom line, she's only four! She's still a very small girl. She's clearly learning to do better (just look at the first 3/4 of this christening to see her doing much better than we've seen from her in the past), but of course she's got more to learn. That's just how it is with young kids.