Oh this is fun!
I agree, probably 3rd gen hybrid. Check the nares. There's definitely military macaw in there. It's tricky because while I see much scarlet, the upper beak is black, not mandible.
I could actually build an argument for first generation shamrock macaw (military x scarlet).
I've got no help for you unfortunately but I certainly wish you luck!
As per the bolded, that was my first thought. Though the more I look I think the stronger argument is for a Shamrock/Scarlett cross.
So, putting on my macaw owner hat:
Hybrids can be really tough to deal with, as they often take on the worst traits of each of their parents. They don't always, but it seems like it happens a lot.
Since you already have birds, you already have a lot of the skills you need, you just need to scale them up for the macaw. The key is patience and gentle firmness. You do need to be in charge, but you need to be in charge in a very specific way. That way is firm and no nonsense, but also gentle and non-threatening.
My biggest piece of advise: Observe your bird. Constantly. Look for even the littlest little clues as to what he or she is thinking. That will help you form a bond with the bird. Once you have an idea of how your bird reacts to things, and when she's happy/mad/irritated/bored, etc, you'll know how to best choose the right time for various activities so you can ensure success. Training a ticked off bird is going to end painfully, so you don't want to start a training session when she's mad. How will you know when's the right time? By observing and notating everything.
Other than that, just be patient. There's no need to rush right into anything. Let the bird settle in a little bit and get to know you. Hang out close enough for her to see you, but not so close that she feels threatened. The first week I had my Charlotte I literally just sat in the same room with her on my laptop and did my thing. The first day I mostly ignored her, except for telling her what I was doing and assuring her it was okay. I gradually added more interaction and got closer to her. These days she's a spoiled brat who loves attention. But these things take time, so don't get in too much of a hurry.