reaching out to bio-mom
I think you're on the right track with not responding to her emails, and that your husband is right that you can't have a civil relationship with someone who doesn't want that. You can let bygones be bygones without communicating that to her. Your actions are already most likely showing her that you'd like things to be civil. If she decides to extend an olive branch, go ahead an accept it, but since you haven't engaged in the pettiness it's not your job to try and put it to a stop. Just keep taking the high road, trying to fix it will probably lead to drama.
My husband's ex had a LOT of hostility toward me in the beginning, and it took quite a while for things to become civil. In the beginning I avoided all contact with her because she could not be civil toward me or toward my ex when I was around, so we thought it was best for my step-daughter to not be in that kind of environment. So pick-up and drop-offs happened without me there (out of sight at first, either staying in the car parked around the corner to pick up at her house, or stayed inside our house and mom picked up at the end of the driveway. It seemed ridiculous to have to cater to her like that, but we really believed that if that was the only way she could be civil during pick-up/drop-off, it was worth keeping my step-daughter from the emotional trauma.
Basically, we just worked our way slowly closer to pleasant contact... one day when it felt like it wouldn't cause her to flip out, we parked in sight of the house to pick up... Then one day I was outside in the yard weeding the garden when she picked up. One day I got out of the car and was silently present during pick-up, then another day I was there quietly at drop-off, having already gotten my hugs and kisses from my step-daughter inside so mom didn't have to see. We inched our way forward, trying to gauge mom's comfort level and trying to choose the right time to push it forward just a little.
Again, it seemed so ridiculous to have to walk on eggshells and tiptoe soooooo slowly closer to normal, and to still continue to minimize contact so it is nothing more than necessary... But in the long run I think it was the right move.It has allowed us to both be at special events for my step-daughter and have it be about my step-daughter and not about the grown-ups. In 7 years my step-daughter has never seen her mother be hostile toward me... I'm sure she's heard some things at one time or another, but her actual experiences of us are all of civility at worst and even friendly at times, and I think that is going to be what she remembers.