I believe that the one-on-one time is actually causing the problem.
Eye contact, with appreciation is all he needs: he needs to be seen for himself, loved as himself and appreciated for his real strengths. He needs it 20 or 30 times a day. Once for an hour or two every few days isn't enough --it's like trying to eat once for the whole week. He may need a reminder that when he was little, you did all this for him, too--and absolutely loved doing it. He'd probably love to hear his birth story, or the stories from the first few months of his life.
None of that requires you and he being alone... and I think even really little kids 'get' that the baby's been put away, regardless of what the baby needs, in order to put in the quota of time that's available for him. That doesn't feel like love, it feels like obligation, difficulty, complexity and it's not a nice thing to feel.
It can help a lot to slow your whole house down to baby speed for a while. You're recouperating from pregnancy, which means you need less activity and more rest. Your kids need time and space to sort out a new relationship in their house (actually, with dh and the kids, it's adding another 5 relationships --one between each of the existing family members and the new baby).
You can't keep living life 'as if' you don't have a new baby the way you did when you did not have a new baby --at least not without someone in the building losing their mind.
If your daughter's homework gets ignored for a while, she's still too young to have her grades count toward Harvard, and she can make up for it later. If your son misses a few days of preschool because you had too hairy a night to deliver and pick up, that's fine, too. He doesn't need preschool as much as he needs a sane, rested and nurtured mother.