Well, if she's not seeking sole parental responsibility, then she obviously doesn't have any genuine fears about the kids being in dad's care. At least, that's how the Court usually sees it.
You and I both know that mum is being unreasonable, as we can both reasonably speculate that the Court isn't going to take well to it.
But dad needs to follow through on the Court process. He's not seeing much of the kids as is, and she's not seeking sole parental responsibility, so it's not like he's going to get less time, and he really has nothing to lose in such circumstances, does he? Besides, he probably won't ever get to trial. Proceedings do have a funny way of motivating people to change their tune, after all, especially if after a couple of interim hearings, things still aren't going their way.