You speak as though Ioan is but a mere bystander in his life. Forced to make the choices he has. But he could have made different choices.
He could have chosen not to move Bianca into his home on his immediate return from his work trip. He had not seen his daughters for months, I can’t imagine this choice was conducive to reestablishing his relationship with them. The children didn’t know Bianca - she was a stranger to them. A stranger who was now living with their father.
He could have chosen to pursue contact legally upon his return from his work trip. He didn’t and it would take him almost a year to do so.
When he eventually did pursue contact and it was of course scheduled to begin immediately, he could have chosen to see his children rather than go to Australia with Bianca and miss his first two contact sessions, in what would have been over one year.
He could have chosen not to be okay with his new partner posting pictures of them on her Instagram whilst responding to comments saying how happy they both were, had never been happier, whilst knowing that his eldest daughter was probably reading these comments and was anything but happy, but was feeling abandoned and replaced.
He could have chosen to understand that his daughter acting out was entirely normal given what was going on in her life, and that she had every reason to be angry with him, rather than inferring that her feelings were not valid and that she needed therapy before he could see her.
He could have chosen to seek the US equivalent of an emergency custody hearing, given his claims his children were now in the sole care of an abusive alcoholic who was unfit to care for them. Absolutely NO reason at all why he couldn’t have done this.
So no, I don’t think Ioan was in a “no win” situation at all.
The current state of his relationship with his daughters is largely by his own hand. He did have choices, and he made plenty of them, it just so happens his choices don’t appear to have taken his daughters into consideration much.