I just went through this same EXACT thing last year! My daughter turned 3 only weeks after my son was born last July. I work full-time and knew that I had to return to full time work when my son turned 12 weeks old.
I decided to continue taking my daughter to school. This was after A LOT of agonizing (just like you). I spoke with her "teacher" at school and the teacher said that, in her experience, older siblings who continue on their normal schedules (i.e. going to school) seem to adjust better. She sees a lot of kids getting new siblings as she "teaches" all 2-3 year olds so I took her advice sincerely. She said that the older sibling's life is already thrown for a loop simply by the introduction of a younger brother or sister that it's best to keep all other aspects of their daily routine as normal as possible. She said that the kids she's seen that take 12 weeks off of daycare to stay home with their mother and new sibling absolutely lose it when they have to return to daycare when mom does return to work.
Believe me, I know the stress. My MIL hated the idea that I was going to take my older daughter to daycare while I was home with my new son which made my decision all the more difficult. But in the end, I honestly believe it was the best choice for me.
When it was time to start taking my daughter to school after my son was born, she didn't seem to mind. I'm thinking she liked it most days because she was able to get more attention at school then she could at home. I was highly aware of paying much attention to her after her brother was born but when you are breastfeeding a newborn, there are certain times that the 3 year old just can't be the center of attention. On the few days when she asked why she was giong to school but the baby was staying home, I just explained that the baby was too young to go to school but in a few weeks, he would start going to school just like her. And then I would ask her if she would show him to his room when he started school and she felt very important. She seemed totally fine with this explanation (and it was the truth). And I just explained to her that all the baby was doing was eating and sleeping (trying to show her that it wouldn't be much fun to be at home with us - which is true).
As for getting both of them out the door in the morning to get her to school, I totally stressed about that too. But I just let things flow and it worked out. I would let my daughter wake up at her normal time. Then I'd help her get ready and wash my own face and put on some clothes. I just did the baby's morning feeding whenever it needed to happen (making sure I fed him at least a little before heading out so that the newborn didn't have a meltdown while at my daughter's school). If the baby decided he needed ot eat right before we walked out the door, I simply made my daughter breakfast so that she could eat while the baby did (she normally eats breakfast at school). I looked at it as "practice" for when I had to go back to work - and it really did help me adjust back into work.
Just try to take some deep breaths and let things happen naturally. The nice thing is that you're able to ease into this without the stress of having to get to work yourself :) My husband also worked a schedule where he was virtually never able to drop off and seldom able to pick up. So I was doing both like you will be.
Once the baby gets a bit older and you both adjust, you can try to keep your son home from school maybe to do a fun trip to the zoo one day. The nice thing about having a newborn in the summer is that they sleep well in a stroller and then you can just stop walking around the zoo to feed the newborn when need be. Then your son will feel like he's having a very special day (missing school AND going to the zoo!)
I truly feel that our kids watch how we react to situations and base their own reactions on how we are reacting. So I think it's best just to try to let things flow and limit your stress. This should help your son limit his own stress. I know that's a lot easier said than done but you will get through this! I know from experience :)