I was worried about the same thing when I brought my daughter home. I had my two buns, Olivia and Bindi. They were a little stressed out at first with all the noise. We have a small house so even though the buns have their own room the crying was still pretty loud for them. I stressed about them stressing, but they were fine. They got used to it.
As for introducing the baby to the bunnies, I just put her on the floor and let them out one at a time. My buns were super sweet so I wasn’t worried. They just sniffed her. Olivia was a big chinner so she chinned the baby a few times. 
And I did my best to make time for the bunnies even though I was tired. I felt bad about that time too. They were used to getting so much attention. Everything worked out though so try not to stress. My Mom kept Everly about once a week and I used a lot of that time to relax with my bunnies. So if you have someone who can watch baby for you, even for a few hours, that will make you feel less guilty if you get in some quality time with your bunny.
One of my first pics of Everly and Bindi Loo
Later on with Olivia:

Sadly Olivia passed away last Spring.
My daughter just turned 2 and her and our new bunny Sterling are great buds. Everly just adores the bunnies.
