Dogs & Cats can't be compared to parrots in my opinion. Parrots require way more attention than other pets. I have had just about every pet you can imagine, and I too never got rid of one, it was in its forever home with me until the end of their life. It has been my experience that a parrot really needs your attention, no different than a child, and yes, they do get jealous and territorial towards their favorite person when they feel threatened by another.
As for the terrible two's.......2 of my parrots went thru it, just like having a 2 year old child. My amazon is going thru her terrible two's as we speak, she turned 2 in April. I can't take my eye off her, or she's into trouble, plus a tantrum of independence and doing what she wants WHEN she wants.
I am sure their are owners out there that have done both, parrots and babies, I couldn't due to the fact that I am the type of person who wants to give all of myself to my loved ones, and would feel stressed and torn trying to give both my young children and parrots the love, patience & attention that I feel they deserve. It's a personal decision for me. Thank goodness I have 4 children older and don't have to face the decision you are making, I would WANT that bird so badly, and not knowing what life with a parrot is like first-hand, I would make the choice to get a bird. Knowing what I know NOW, in hindsight, I wouldn't.
Best of luck to you & your husband in your decision. I am sure you will do what is right for you.