You'll probably be the best judge because every tot is different. If you really think it will throw her for a loop to see you in the hospital and it will be too traumatic, then maybe it's for the best if she stays home. If the only thing you're worried about is having her cry when it's time to leave...don't worry, as long as you keep the goodbyes short, she'll stop crying probably by the time she's in the car. The saying outside my daughter's classroom is "quick goodbyes leave dry eyes"...pretty true.
It might be less confusing for her to see you in bed with a brand new baby and the hospital than if all of a sudden you walk through the front door with a baby...like you just got him/her at the store or something.
My daughter was 3 when we had a new baby. So, she was a little older, but she got to wear her new "I'm the big sis" shirt. I also went shopping ahead of time with her and let her pick out a blanket and a stuffed animal for the new baby, which she brought to the hospital. Once she arrived, I also had a gift from the baby for her. So, it was an exciting time with fun things surrounding both kids.
Congrats on the new babe! Have fun!