Because he's a dog, Enzo doesn't get to go to the hospital to hear what the doctors have to say about Eve. Enzo laments this fact, saying that nothing was expected of him except to do his business outside and to stop barking when told to stop.
Enzo is somewhat jaded by his existence as a dog in this situation. He's denied the opportunity to listen or communicate, and is reduced to doing only what we might consider normal dog things.
Eve stays in the hospital for weeks. Denny cares for Enzo and Zoë, and visits Eve regularly, and these tasks take up all of his time. Enzo describes how their schedule changed from spontaneous restaurant and coffee shop visits to regimented days with bagged lunches and dinner at home every night. Enzo says that while not colorful, it was efficient, which was all that could be expected considering Eve's illness. Enzo's walks and trips to the dog park are infrequent, and he receives little attention from Denny or Zoë. Enzo tells the reader that despite this, he was willing to make the sacrifice to preserve the family dynamic and for Eve's sake.
The reader understands that Eve is likely extremely ill given the length of her hospital stay. However, Enzo's narration focuses on how those at home are affected by Eve's absence, and particularly the sacrifices Enzo chooses to make in order to help Denny. Notice that Enzo doesn't mention the sacrifices that Denny is surely having to make with this arrangement, which further illustrates Enzo's non-human understanding of events.
After two weeks of their regimented schedule, Maxwell and Trish offer to take Zoë for a weekend to give Denny a break, and Eve supports the idea. Denny is hesitant but agrees. He and Enzo do everything they used to do—jogging, watching movies, ordering pizza, watching racing tapes. They go to the dog park to throw a tennis ball, but a surly dog gets after Enzo and Enzo isn't able to retrieve the ball. Enzo says the absence of Eve and Zoë feels wrong, and that there is no joy in their day—something is missing.
Despite his initial dislike of Eve, Enzo's world is turned entirely upside down now that she and Zoë are removed from it, even just for a weekend. It's indicated that they are the bringers of Denny and Enzo's joy, the joy that is missing over the course of this weekend. We see how Enzo has gradually accepted Eve into his life when he makes this realization.
After dinner, Denny stands up, takes Enzo outside, and then says he has to go see Eve, telling Enzo to stay. Enzo lies down in his bed, and Denny leaves. Several hours later, Denny returns, crawls into bed, and tells Enzo twice that Eve is going to be okay.
Enzo, being a dog, can't go see Eve. We can't know what happened at the hospital, but Denny's statement makes the reader question whether he's telling the truth or "manifesting."