In NYC, the privates and hospitals alike can run 8's, 12's, and 16's. In NY it's illegal to work in excess of 16 hours. My old hospital, North Shore LIJ, had all sorts of start times for their interfacility division, such as 0500-1300, 1200-2000, 0600-0600, 0900-0100, 1900-0700, 0000-0800 to name a few. The city tours are either 12 hour T1's or T2's, or 8 hour T1/2/3's. You can double up for a 16. FDNY EMS does 8 hour shifts only. T1 is the overnight, subject to night diff, and starts around 0000 hrs, give or take an hour or two. T2 is the daytime tour, typically starting around 0600-1000. T3 is the evening shift, starting from 1100-1600 or so. This is also subject to night diff.
An employer may accomidate you initially, if you're lucky. However, if you rub someone the wrong way, or if they want you out for some reason, all they have to do is change your schedule to conflict with your personal life. Keep that in the back of your head.
At least at NS-LIJ, you could work three or four day weeks - maybe two 12's and a 16, a 16 and three 8's, or two 12's and two 8's. You may only need to pay for child care three or four days a week, instead of five. regardless, if you're a single parent, you'll need family help to do it on an EMT salary. Child care expenses will quickly wipe you out. A good rule of thumb is to not have anything planned, or anywhere to be for at least three hours past the end of your shift. Late jobs are more the rule than the exception in some places, and can easily run in excess of an hour past your off time.
I used to work the Sat T1 (Fri night-Sat A.M.) 0000-0800 IFT, 46Y Sun T1 (Sat night) 2000-0800, same thing for Mon night, and the Fri T1 IFT (Thu night), 2200-0600. My wife and I used child care on Mon, Tues, and Fri, since I couldn't make it home in time to watch our child, and I also needed rest after working the busy overnight.