for the crown do you only get the power of two standing stones when your wearing it.
Not necessarily, and is worth some personal testing.
I currently have the crown in my inventory,
not equipped, and the two chosen stones are shown as active on my Active page.
1. Initially it would remove the previous stone when unequipped and the Active page would reflect this.
2. So I unequipped the crown, chose a third unwanted stone, then went and chose what would be my secondary stone.
3. I then travelled to my primary stone, chose the stone,
then equipped the crown.
4. After unequipping the crown, both my desired primary/secondary stones remain active.
We don't yet clearly know if you need the crown equipped or just to choose your stones.
Whether glitch or intended gameplay, my current Dawnguard character has two active Standing Stones
and is wearing a helm, not the crown.
Time will tell but, for now, perhaps you can try the above steps for yourself and see what happens.
Hope that helps