Wait

Yes

I can't wait for him to die fr

No his daughter is still alive

We don't know if he sent someone or he himself killed the wife. I wouldn't be surprised, but from what we saw back then is Chang Geon was really going to wish him well and say goodbye. He just wanted to have him by his side.
He crashed out was valid considering everything, but I don't know if he would go as far as killing his wife. He's obsessed with Samyeong, but was waiting for the right time to invite him to the palace.
Samyeong's did say that the next time he will see him would be when theyll be able to show each other their accomplishments. And Chang Geon understood that.
It looked like the wife was slaughtered, but idk... We really do not know who killed the wife. For all we know, it could have been the oldest prince to get things moving so someone could control Chang Geon. And Samyeong would be the only one who could.
Idk! It's a mystery.
I don't think the daughter is dead, though.

We actually don't know for sure, I've reread the whole manhwa and there isn't a single instance where it mentions it besides the strange panel from this chapter, but it is still not enough to say CG killed his family