i think you can protect yourself and the kids while also acting from your best self but it is true that the D process is no friend to positive changes in the R..
could it be that H is coming from a place of fear about his future that blurs his sense of what is fair? and could his underlying guilt and fear (that he is unaware of) about how the D will impact the kids cloud his view of you concerning custody? i say this not to mindread but to perhaps see if a different frame may help you..
so you are protecting your own and the kids future from this person who can't see well, that is what you distrust, not him... and so that you are not internalizing his view of you during this which also comes from this place of not being able to see.... and so that you realize that there is nothing you can do to change how he sees you right now, no matter how hard you try, he sees you through the lens of his own guilt and fears.
you are not being adversarial or judging him unfairly then, you are just realizing that he is not able to see clearly right now... and you are aware that it is hard for you as well to see him clearly, which is why i think you continue to check yourself with others and here about doing the right thing... that is kindness, KG.