OP, I realize that you've been through a lot, but take a step back and B-R-E-A-T-H-E. Nobody on this forum IS the system OR the mother you are fighting against. We are here to provide help, and it's harder to offer that help when you respond with snide remarks and say we "have no clue". This isn't a site where people just make up fake legal advice to upset parents in crisis.
I did some investigating about some of the things you've mentioned, and talked to my sister in law, who is an attorney in CA. (I can never ask her my own question's as she is ex-hubby's sis.) It appears as if there is quite a bit of backlash in CA over the voluntary acknowledgement form. Nurses and midwives are even bound by law in some counties to offer it to unwed fathers at the birth. The CA.gov website touts it by claiming that it will offer children and fathers of unwed mothers "financial support from both parents, access to important family medical records, access to the non-custodial parent's medical benefits, and the emotional benefit of knowing who both parents are". Unfortunately, that paternity acknowledgment DOES NOT establish legal or court recognized paternity, and may in fact establish the MOTHER’S custody without due process (administratively designated custody). This effectively signs dad up for child support without establishing visitation or custody. Even the website for the DA in Riverside County states (while trying to be positive) that "In most cases, signing Voluntary Acknowledgement of Paternity form will make it easier to establish paternity in a court."
The other problem with this form is that mom can have you removed. Also at CA.gov, "Either parent wishing to cancel or rescind a filed Declaration of Paternity can use a Declaration of Paternity Rescission and need only notify the other party by mail". Now OP, these may already be things you know, but I think it will benefit others to have this info up.
Now that you know that you won't be able to force them to move back to CA, and that's even *if* she left illegally, you have a framework to work within. YOU can have the courts make DNA paternity testing happen. You petition for it, don't wait for a judge to think of that idea him/herself. This is an everyday procedure... nothing to say "You've got to be kidding" about. Once paternity is established THAT way, you will be able to establish your custodial standing, whatever it may be, and visitation. But be prepared to know that if you've been spewing accusations of human trafficking, corruption, and abduction, the court is likely to ask that your visitation be supervised for some time. Obviously, supervised visitation would be easier if you moved there again.
Battling with my former spouse over being able to see my kids is what brought me here as well, and I have also had one of my children pass away. It is very sad for a parent to be separated from their children. I realize that it's easy for the claws to come out and to feel defensive when anyone suggests anything other than a situation in which you have ample access to your children. You have a hard road ahead of you, and sometimes we all need a reality check along the way by others who have knowledge of how the system works, even if that knowledge doesn't confirm whatever our desire is.