I'm with your husband on this one, and I have been through this. We had a corgi that was very poorly bred, very nervy, and a rescue. We got pregnant unexpectedly and knew we may have a problem with that dog and the baby. She was fine until the baby started walking, then it was the same as you describe, growling if my son came near her, unprovoked, and when we scolded our son she would come running from out of no where to nip him (she actually nipped a friend's toddler). This dog was not clear in the head. Yes, I could have trained her, hired someone (this was before GSDs, SchH TD's etc), kept them separated, etc....She eventually nipped at my son, and that was it. We have a zero tolerance in our house for unprovoked aggression towards children, doesn't matter where it came from...it was completely unprovoked and a result of terrible genetic instability. I rehomed her to family across the country. Paid to have her shipped to them. She's doing great, happy as can be, but cannot be trusted around children.....and that was a corgi....if it had been a large breed like a shepherd, I probably would have put her down. As harsh as that sounds, the safety of children everywhere is priority, and genetics are genetics.
I asked my TD about her after I started training. TD said she would have probably suggested putting her down. The dog had great obedience, but was very very nervy and fear aggressive. I know lots will probably give you a long list of things you could try, and at the minimum I would say get a trainer experienced in fear aggression to assess the dog. I looked at it this way, if my corgi bit my child, left permanent damage, scaring, etc...I would never forgive myself. Also, if I trained, spent the money, environment managed, etc...I would never trust her, would resent her, and the relationship would not be a healthy one. I know a lot of people judge me for rehoming her, but I could care less. My husband has scars on the left side of his face from a terrible GSD bite when he was a boy. From a dog that "never hurt a fly." It's one thing if we are talking about adog, taunted, tortured, or teased by the child, but this seems like what I dealt with, unprovoked, unstable, unclear, responses...as a result from poor genetics....but def get a professional opinion by someone that can witness the dog in person.