You might cross-post this in the behavioral section as I know there are some people with a lot of behavioral interests who visit there that may otherwise miss it here.

My thought it is less to do with dominance and more to do with insecurity. She's been shuffled around and and had to deal with who knows what, and she is generally insecure. She found a spot where she felt comfortable and secure, and she immediately felt the need to defend this and keep it from being taken away. My thought would be along the lines of what Vela posted, in giving her own spot and setting her up for success in that she is not in a situation she feels she needs to defend her spot. When she is in her crate I'd leave her undisturbed, letting her come out when she wishes. Let it become her safe spot and haven, a place of her own.

I would avoid punishments if possible, i.e. the squirting, as it could serve to increase her distrust and insecurity. I think I'd keep a little treat pouch on me, and focus on rewarding good behaviors. Starting out simple, like saying her name, and when she looks at you toss her a morsel. Then maybe moving up to calling her, and if she comes giving her a treat. I'd take her out for little walks with just you and her, as I have found walking to really be a bonding experience for many dogs. I know my Tasha, who is very distrustful of strangers, tends to begin accepting and trusting people who have walked with us.

I'd definitely not let her have access to any beds of furniture for now in which she might again feel the need to claim and guard it. I would work on gently building a trusting relationship while doing the NILIF with any toys, food, and so on. These are some of my thoughts on the situation. I know there are others who might have some good ideas to try too.