My wife and I gradually took over parental duties. First, they taught us how to change a diaper. It was a two-person job -- one to make the change, and one to hold his guts. My very first diaper change was done in the shade of my son's own liver. Suck on that imagery, T.S. Eliot.
Diaper changes are gross no matter how many extra body parts are involved, but how many parents have to change an organ sac dressing? The doctors did it at first because the risk of infection was high, but after a few days, the membrane got scabby, like your knee a week after skinning it. Here's another photo, if you're brave. So twice a day we would cut off the dressing, clean the sac, apply new gauze, and wrap it all up. Before long, we were pros, casually cradling our child in one arm while his intestines rested on the other. Even simply holding him had a learning curve. We couldn't sling him over our shoulder, because then his belly would compress against us and we'd get all tangled up in stomach.
Playful belly button raspberries are completely off the table.
To treat an omphalocele, you wait for enough space to grow so the organs can be stuffed back in where they belong, like making room for seconds on Thanksgiving. In the meantime, parenthood is one long panic attack. We were sent home with a tiny inside-out child on supplemental oxygen, a feeding tube, and positive thoughts.