From personal experience. My hubby was on leave for 4 days after we check out of hospital stay. He didn't do much since he wasn't confident to handle dear son. My mom had to take charge. Besides, newborn babies are easier to look after as they're asleep most of the time.
CL: I've never hired CL but have faith in her since am sure you've done your homework by asking opinions on her performance. Have you mom or in-law to drop by from time to time to check on you guys.
Check-up is normally after 2-3 days after hospital stay.
Our dear son is 8 mths . Save that precious leave for family outings/couple dates/check-up etc...