No, as already said it was not a Deus ex Machina.The cost of the deus ex machina was his grandson.
That's hardly great writing; it's clear to me they wanted to have Jack do something like that so it could look dark and tragic.
Well of course they did, that's what writers do. They have an idea about a story and what they want the characters to do and then they write it down.
To me the story was overlong, a bit boring in places, and flawed in its premise.
How was the premise flawed?
And the PM was unrealistically twunty just so we could have Frobisher do in his family for the sake of more manufactured tragedy.
The cabinet scenes were extremely convincing and Frobisher was well realised character. He didn't kill his family because the PM was a bit mean to him, he killed them to save them from the alien abuse and then killed himself because he couldn't live with what he/his life had become.
Children of Earth was what Torchwood promised from the beginning. Adult compelling viewing and one of the best shows the BBC have produced for a long time.
I can understand people not liking it because the tone was too dark and didn't sit well with them, but it was not boring.
It was compelling and we have not had a science fiction show like CoE for a long time and it will probably be a long time before we a get a show that good again.