S.H.
My son is 5 and naps in the afternoon.
He still goes to bed at night just fine, by 8:00-8:30pm.
My 8 year old daughter goes to bed about the same time.
Both my kids wake up on the morning by 6:30am.
They went through temporary phases of waking up earlier.
It is temporary.
I, go to bed whenever.
My Hubby too.
So, THIS is when, after the kids go to bed, that me/Hubby can have any alone time.
But for you, you get up at 5:00am.
Me, even if I don't have to, I am awake too, very early in the morning like you. But I don't need much sleep to function.
Or, make your 3 year olds nap, earlier.
When is he/she going to nap anyway?
My son naps in the afternoons, even at 3:30 on school days, and he naps for 2 hours. Still goes to bed at night just fine. Earlier than 9:00pm.
And do the bedtime routine/bath, earlier for your 3 year old, even an earlier dinner. So that he is already set for bed, earlier. And make everything dark and quiet... 1 hour before the actual bedtime. To 'cue' him.
Does your 3 year old need the nap?
Because if not, she goes to bed at 8:00pm.
But you said you like time with the baby when your 3 year old is napping.
So, back to square one.