I realize I am overthinking this, so please forgive me

My DD is 3 and goes to daycare and loves it. Our plan for my time in the hospital is to generally have our family help out, but they know that as long as everything happens during the week - they can make the decision to have her in daycare during the day (it's "camp" time and they do fun things so she loves it) or just opt to keep her home with them.
My husband and I were discussing today, if the coming-home-from-the-hospital day falls during the week, is he going to have her go to daycare and just the three of us (DH, me, new baby) come home... or would he bring DD too? He seemed to feel it would be easier to have her in daycare (which it would), but I'm just wondering whether it's somehow... for lack of a better word... psychologically better for her to be a part of that. She is very excited to be a big sister, but I'm sure she has no idea what she's in for. Is it more "Huh?" for her to arrive home from daycare that day to a baby already in the house and now that's just how it is... or do you think it helps her adjust to help us bring the baby home, help get him set up, etc.
I feel like I lean towards having her be a part of it. Wondering if any STM+ have thoughts?
Re: File this under: Overthinking it - bringing home baby
I have a three year old too, so I get it:)
I will say we are bringing lo home and then dd will come out to the car and help bring her new sister in:)
Thanks!
As for bring baby home, I'm not sure but we will either have DH pick DD up and then come to the hospital to get DS and I or the three of us will leave the hospital and then pick up DD at daycare (providing the timing works out). Hmmmm... lots to consider. I like the idea of a balloon for DD the day we bring DS home since she loves balloons but we do already have a big sister gift for her from DS (an Octonauts playset that she is going to lose her mind over), I just have to wrap it.
I'd be nervous of going home with baby first and then having elder sib come in afterwards feeling left out and displaced.
BFP#1: 08/30/12 EDD 04/30/12 m/c 09/04/12 6wks
BFP#2: 01/27/13 EDD 10/06/13 missed m/c 02/25/13 9wks
BFP#3: 10/30/13 EDD 07/05/14 Our little dude was born on 07/10/14 @ 2:19p