Personally I would if it was at all possible I would. You could feel really awful for a while though so tending to a baby, while been woken all night in hospital while trying to recover will be hard. If your H can stay too, at least even for the first night, then I'd say go with that. And you'll likely need him there during the day to give you as much rest as possible.

I stayed in the hospital with my son for 6 days when he at an operation at 14 months old and I was shattered when we left. It was exausting and I got barely any sleep (even with naps during the day with my H there).

Good luck