Z., it's hard, but it's time to send your wife out without you and baby as often as reasonably possible.
Once you are sure your little girl is fed, dry diaper-- creature comforts met, not a hungry, tired kiddo-- have mom hand baby off to you. Mom should do what we ask preschool parents to do: smile, say "Mommy's coming back! Have fun with Daddy!" and *cheerfully* leave the house. Watch her walk out the front door. Wave bye-bye.
And let the tears come. You are breaking her in to not having mom 24/7. She's developed mom as an essential 'habit'... now your daughter has to learn that mom can come and go and that she will always come back. That's the goal. Make sure your wife leaves for at least 10-15 minutes, but not too, too long. Your daughter is old enough to understand object permanence (that things can go in and out of one's view-- "disappear"-- without being gone forever.
The goal is to teach your girl that mom is going to come back. Honestly, I have done this hundreds of times with children I have cared for as a toddler caregiver, preschool teacher and nanny. Kids whose parents leave confidently tend to recover a bit faster. Kids whose parents linger and don't leave, keep coming back to comfort, etc-- those kids have a much harder time. Our children need us to guide them during these new transitions and learning experiences. So, when your wife goes out, make it a quick exit. And then you, you work on helping baby soothe herself. Take her to look out another window (where mom isn't), hold her in your lap and look at one of her board books, some babies like to be packed around and get a 'tour' of different things in the house from the adult-sized view. "Ah, here's the freezer. What's in here? Shall we see? Oh, look, some frozen cherries. Can you feel the cold?" Distraction, distraction, distraction.
She may still cry, but the more you practice this, the better you will both be at this. Crying for mom for 20 minutes will not harm your little one. Mom comes back! We can be sad and then be happy again. It can be a hard thing for a baby to learn, but sooner is better.
(and please, don't feel bad for not starting this earlier. We all do what we think is best until it stops working for someone, and it sounds like "Mom Only" has stopped working for your family. Good luck. And get some earplugs. You'll still hear her, don't worry, it will just take the edge off. :) )