Oh I'm so sorry about your pain!!! You must be so heart-broken. I know you loved Braxton dearly, and you have been an awesome Mom to him. You adopted him from certain death 3 years ago and gave him a loving home.
It must have been so difficult to be put in that predicament. You asked a vet's advice and it's understandable that you followed that advice (sometimes it's also extra-confusing when family is sort of telling us how we should feel and what we should do. I'm 41 and I still tend to lose sight of what I want if my family is swaying me because they're so controlling).
Since Braxton had had a history of aggressive behavior, it's possible that he could have bitten again and caused serious injury or death. Of course, Braxton wouldn't have
intended any harm (and I'm sure he did love your daughter), but there was probably something in him---either a hereditary thing, or something as a result of early abuse from a former owner---that he didn't totally have control over. And since it has been a long-standing behavior, it's doubtful that it would have gotten any better.
You really acted with good intention, and Braxton understands! I'm sure he doesn't blame you. Very very few people would have adopted a special-needs dog. He probably couldn't believe his luck! He is now experiencing only bliss---no sadness whatsoever. Thanks to you, he got to experience the height of earthly love.

Now, he's enveloped by such love we can't even imagine, because it's the ultimate. There's no physical or emotional pain for sweet Braxton. I believe that with all my heart. He's fine and wants you to be fine. And you will be reunited when it's your time! For now, experience as much love as you can--with your daughter, your other dog. And don't feel bad if you need to take a break from your family. It doesn't sound as if they're particularly sensitive to the love of a precious pet.
Keep coming to this board for support. We're all here for you!!
Sending you comfort and love,
Little Girl's Mommy, Kathy