Rescued two quakers

I acquired two quakers a little over a month or so ago. They were in a terrible situation. The woman said she only had these birds for a couple of months but knew she couldn't keep them because they were stressed from all the activity going on in her house. She has small children (poked at the birds-I found a crayon in the cage!), dogs, & tons of other birds. The filth was awful. One of the birds is now bare chested-it plucking was what made her decide to give them up.
I've since read that quakers are cage aggressive. They go crazy whenever I change food/water. Is that pretty normal? I'm not familiar with quakers. I have had them out of their cage a few times & once they're away from the cage, they're pretty mellow & quiet but I think they've been so traumatized, I'm thinking I should leave them alone. I had surgery on my right thumb so I've left them alone (except for changing cages) pretty much. I just don't want them to get so used to not interacting that they'll never want to be handled.
I was told these birds are a proven breeding pair & I'm wondering if that's true, maybe they've never been handed much.
Sorry to go on like this. I feel so bad for them.
Thank you for any help you can offer.

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Sorry, I'd meant to add some pictures of my birds. I've yet to name them. I feel bad about that.

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I don't know anything about Quakers but I'm sure you will get some great advice here. They are gorgeous though!

I once found a Quaker when placing my bus in the parking lot...walked right up to me while on Long Island; Strangest thing ever happen..

being a proven breeding pair means they have reared young before so they have bonded together and you may have to deal with babies in the future.

Combined with the trauma the fact they are bonded means they will never truly be as trusting as companion parrots and they will almost certainly be more territorial. All you can do is work with them slowly, the fact you've had them out of the cage and perching on you is a great start especially for birds in that situation. Just go at their pace and don't try to push them any further than they want to go. You've got to earn their trust of humans after living in such a horrid situation. Why the previous owner would let the children terrorize them like that I have no idea.

Amazing job at rescuing them and deciding to work with them, they're very pretty.

I'd take a look at some of the posts in the breeding forum asap so you can be a bit prepared if they decide they're going to have babies

Bacca (my Quaker female) was pretty territorial about her cage when we first "rescued" her as well. Oddly, she would just come out and be real friendly on your hand or finger or a perch, but yeah she'd freak out if you'd reach in the cage while she there.

She got over it with time.