The father just said and tested it in the previous chapter that threatening him doesnt work so even if they used the eyes to expose everything Able would still die of the poison since he wouldnt give that up so they are between a rock and a hard place trying to figure out the poison before Able dies or Vincent gets executed since no parent will immediately sacrifice one of their kids for the other (Honestly he knows his mother's powers do you think he would do this and then go "Ah dang ya caught me guys. here's the poison time to pretend this never happened")
Honestly I think the plan is/was (Dont know for sure but this is just a guess)
Poison Able for leverage
Frame Vincent since he is getting too strong too fast
Get him isolated in a cage where he cant use his power so the pirate queen can kill him ahead of the execution date incase the family decided to pick Vincent over Able and expose everything
Now that Vincent is dead exposing Carmen wouldnt save anyone so now it becomes a "Make me the head/successor or your other son dies too" situation
Plus depending on how much they still care about Carmen as parents after this it becomes a is revenge worth basically 3 of their sons dying in a day type thing.
