He trusts her to defeat his arch-nemesis in a year-long propaganda war carried out in hell on earth, but he's unwilling to acknowledge that he doesn't, in fact, think she's second-rate.

Martha says that she spent a long time thinking she was second-rate -- not that the Doctor ever thought that. Thinking she's second-rate is Martha's issue, not the Doctor's -- because, after all, he trusts her to carry out the plan to defeat the Master, and that's just one of several times he shows her trust and respect. I read that scene as Martha's final realization that she's not second-best -- the Doctor doesn't need to realize that because the Doctor never thought that. He's not the cause of Martha feeling that way -- it's her unrequited crush.

He condemns the Family to a series of eternal tortures, which certainly is playing God, because the universe isn't safe with them alive and he doesn't have the stones to execute them.

I totally read that scene differently. Considering we've seen Ten actively destroy or set up the destruction of antagonists ranging from the leader of the Sycorax to the Cybermen, the Daleks, the wire, the Beast, the Racnoss and her children, the plasmavore, the Carrionites, etc., I don't think Ten lacks the ability to kill if necessary. The Doctor could have easily allowed the Family's ship to blow up without giving them the warning to run, similar to the fate of the bad guys in School Reunion. I think he gives them that warning because he thinks death is too easy on the Family, considering they're going to die inevitably in three months or less anyway. I think the Doctor wants them to survive so he can punish them the way he thinks they truly deserve. This Doctor can be pretty damn dark.