I used to work 11pm to 7am, starting on Sunday nights and off for the weekend on Friday morning.
I also had hubby and 2 high school boys at home.
I did all the normal stuff we all do, just on a bassackwards schedule. When I got home from work I did the stuff anyone working days would do, picked up the house, laundry, etc. Put together everything for supper so it was easier to fix later.
I went to bed about noon and slept until 6. I was able to spend the evening with the family before leaving about 10:30 to head to work.
Supper was breakfast for me and I packed a light lunch and lots of fresh veggies and cold snacks like sugar free jello. I worked in a factory that makes telecom wire and I ran a machine that cabled wire and is longer than a basketball court, so we didn't have a set lunch or break, it was grab it when you had time. Lots of walking and physical labor. Plus it was hotter than the hounds of he** in there so we all drank gallons of water.
When I got home from work I'd have a bowl of cereal or soup or something light like that. Kept the munchies at bay until I went to bed.
The toughest part was shifting gears for the weekend. The boys were in sports so we always had games on Friday nights. Usually I didn't go to bed at all on Fridays until after the game. That helped me with changing up for the weekend. If I slept on Friday during the day, I didn't want to go to bed when we got home.
Once in awhile on a Friday in the summer I would stop at the quick trip and grab a 6 pack. Boy did I get weird looks from all the 7am coffee and donut buyers. One guy actually remarked "a little early ain't it?" I explained I had just came off 8 hours of night shift and it was happy hour and the weekend for me.
One thing about the exercise, does you employer have a rehab/PT unit that would let you use their equip? One of our local hospitals, will let employees use the equip in the PT unit if a patient doesn't need it. Another thought, you have the option of heading to the gym a bit later in the morning, when it might not be as busy.

Or depending on what time you have to be to work, a gym is usually not as busy later in the evening.
I remember keeping to a routine, especially during the week really helped me cope. Going to bed at the same time, even if I didn't feel tired. Getting up at the same time, so I wasn't rushed, and could see the kids and DH. It takes some getting used to and it was hit or miss for awhile, until I figured out what worked for me.