Hi Jim
The SM72485 is only suitable for small currents (around 150mA). You need quite a bit of current at 10V, so you may need to go for a non-integrated supply (i.e. controller + MOSFETs). Get one with synchronous rectification as it will be about 3% more efficient than a Schottky diode regulator.
It sounds like you want to switch the 10V output off at night. Is this your charge current to the battery stack?
If you have the 10V rail switched off, and need the 5V and 3V3 rails to be on all the time, a good start is a buck regulator for Vin -> 5V, and then a buck for 5V -> 3V3.
If you have the 10V and 5V rails switched off, then I suggest:
Vin -> 10V, 10V ->5V (switched)
Vin -> 3.3V (always on)