Yup, whoever you are you are seriously getting mixed up with the characters. Claudio doesn't have children, matthew and maria are his brother and sister. They are all Coheed's children.

After Mayo approaches Coheed, he tells him about the Monstar virus which is in him. He tells him that it has been passed down to his children and will mutate into the Sinstar if he doesn't kill them. Mayo gives him poison and drops him off at home, where he is set to the cruel task of killing his kids.

"debate to understand that we all have a flaw
then fail to represent you life as you know it"
- Coheed explains to Cambria what must be done

"pain is only a pose if you just stop feeling it
you might be able to use the very things that makes us up"
- Coheed realises that he has to kill them and that it's for everyones own good

That's pretty much it.