Quoting L♥vey:" I think my son would resent us bringing her into our home. I think my husband would be completely overwhelmed ... [snip!] ... to everyone. . I appreciate everyone's input. (I wanted to add she turned 5 in November. I forgot how old she was.)"
Your son is 3. I doubt he will resent her. He is of an accepting age. Plus, it is not like you are replacing him. If you think he will resent her, he will do the same to a new baby. Same difference at this age.
Even at 5 she is still moldable (she is a very young 5). She is screaming because she needs stability, love, structure and a life that she hasn't been given. Her father died while she was young. Yes, she has had a bumpy life. Imagine what it must be like to be shuffled and not have a place to call home. It isn't really a matter of "control" so to speak. It is really a matter of her knowing that she is going to be safe and understood. In her short years she has experienced so much. I can imagine that her gramma isn't one to provide the discipline and structure that she needs at this point. She is likely compensating because of the loss of her son. In turn, this little girl is litterally screaming for a normal life. All kids crave structure and routine.
CPS will not take her for simply screaming. That is not something she needs to worry about. Where in AZ is she? Phoenix (you said she is 4hrs away)?
Do speak with your pastor. Like I said before. It takes a special person to be able to love a child as their own that isn't especially one that has needs.