No matter what TB was involved in, including criminal activity, it is not a justifiable motive and TB didn't deserve to lose his life anymore than HDB did. But after hearing CD's fathers comments about TB I don't think TB was involved in anything anymore, because CD's dad probably wouldn't have allowed him to have custody of HDB if he knew he was doing bad things. JMO
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No one deserves to be murdered. No one. Even killing someone in self-defence is closely scrutinized by the courts. A plea of self-defence has to be proven in court to the satisfaction of the judge or judge and jury.
What went on the night of the murders? We don't know. LE obviously believes this to be first-degree murder (premeditated, or murder in the course of a specific criminal activity); please see link.
https://en.wikipedia.org/wiki/Murder_(Canadian_law)
It is not uncommon for LE to lay a second-degree murder charge, then upgrade the charge to first-degree later as evidence leads in that direction. All of this must be tested in court. For LE to charge DS with first-degree murder right out of the box, they must believe that DS took action against TB and HDB. IOW, LE must believe DS was the aggressor and initiator of the violence. He went to TB's house. TB was not murdered in DS's house.
I agree that the neighbor SK is likely key to this, but he may have been instructed by LE or a lawyer not to talk. For all we know, SK could have been the one that reported the van speeding away and hearing HDB.
Custody decisions are up to the courts. If KD took issue with it, he would have to make his case in front of a judge at a custody hearing. CD could also take issue with custody at a later date if some issue that would be harmful to HDB came up. So even if KD didn't like the custody arrangements (and it sure sounds like he didn't), he had to accept them. It sounded like CD and TB had reached an arrangement acceptable to both of them.
CD did not have to use the Blanchette name for her child. It is up to the mother to make the naming decision in Alberta. She chose to give her daughter the Blanchette name, which indicates to me goodwill on her part, and a desire to have her father's child involved in her child's life.
ETA: I am not clear at all if there ever was a formal custody hearing. CD and TB were never married, and I have not heard anything about how long they lived together WRT how courts treat children from common-law partnerships. A formal custody arrangement would allow less ambiguity, IMO, so less opportunity for family members on either side to butt in. There may have been nothing in writing, and no custody order. If there was nothing formal, and TB and CD were both satisfied with how things were working, then it was entirely up to them.