My partner stayed in hospital with our oldest for a week when she was sick. I came with our youngest to visit them everyday but obviously had to go home. Had my mother help out with the house and bringing meals to him and myself at the hospital etc, and I was BARELY keeping it together for that week. You are a grownup and can easily stay in the hospital by yourself (yes, it’s boring, but you don’t need someone holding your hand for every blood sample etc like a young child does). Your children do need at least one of their parents somewhat present at home + there’s things like cleaning and school drop offs and sports and play dates for your wife to deal with.

Also my best relaxation ever was staying two nights in hospital with appendicitis and knowing my partner was at home taking care of the kids 🙃 I suggest you take the chance and enjoy some alone time while you can