I just have a few questions if you don't mind?

If he works Lates what time does he get home?
Is he normally up at the same time as everyone after working a late shift anyway?

Personally for me i look at it this way - if he has worked a late shift (ie until midnight or beyond etc) then i would be letting him sleep in in the morning as he'd worked all night IYKWIM.
If by chance he works til say 8pm and is home in bed at the same time as you then i don't see there being an issue in asking him to take them to activities whiel you stay home and get some cleaning done.

At our house DP is up early and home late up to 7 days a week, the morning and bedtim routines are all mine and i've had to adjust how i do things to make it work, even when he's home there is no big change and he's normally getting a nice sleep in while i run around like a headless chook keeping the kids from attacking him.
I guess you both need to set out what will work and what wont in regards to if he needs extra sleep, what YOU can & can't do when he's taking a nap or if you need him to take the kids etc.