Glad to hear you are having some success in your case.
In David's case, as in many/most, the very limited access he got in Brazil prior to his child's return home was just for show and was never intended to last nor foster a true parent/child relationship. And, in fact, it didn't last and was accompanied by denied visits and parental alienation (every interaction a parent has with a child is an opportunity for an alienating parent to spin, manipulate and redefine the encounter in negative ways in the mind of a child.)
Because of this, many LBP's forgo access altogether to prevent their children being subjected to all the corollary baggage and abuse that comes with it (in some extreme cases every visitation is accompanied by false accusations of sexual abuse, which are never punished, but result in the child undergoing extensive and invasive examinations and interrogations.)
The fact remains in such cases though that access to our children is a privilege that can be taken away at any time by the capricious whims of their abductors.
If parental rights are subject to the discretion and coverture of the other parent (or any other agency/institution) they are not rights. A right is unalienable or it does not exist. Same principle applies to the child's right to a meaningful relationship with each parent.
Without even the barest modicum of parental authority you are not a parent in the full sense of the world. More like a "Disney-Land Dad" and a visitor/spectator in your child's life (which can be better than nothing if, and only if, there's not an ongoing campaign of parental alienation that is being facilitated by the system and harming the child more than your very limited presence is helping them.)
One of the key roles traditionally played by fathers is that of setting boundaries for children. That's impossible to do when you have no authority or when the other parent takes a perverse joy in undermining everything you do in their effort to denigrate and destroy the "non-custodial" parent in the eyes, heart and mind of the children.
Children tend to figure out pretty quickly which parent has the real power and authority and which is a lame duck with no paternal influence. Such parents become babysitters who pay money to take care of children that actually belong to the other parent in every way that matters. Respect for such powerless parents from children, even as human beings, much less as a father, can become as distant as the child's memory of an intact family.