Why would Danerys kill Tyrion? Was he really close enough to the death of her family to be worth killing?
Probably because his brother (Jamie Lannister aka The Kingslayer) killed her father.
Robert Baratheon wanted Danerys assassinated. Ned Stark was against it. Through information from Danerys’ aide, Jorel, Robert Baratheon sent an assassin to poison Danerys. Jorel saved Danerys. Joffrey Baratheon, a protege of the Lannisters, inherited the throne and Danerys’ plot for revenge.
Thyrion is accused of poisoning Joffe, so Danerys will probably turn on Jorel and provide Thyrion with protection.
Robert Baratheon wanted Danerys assassinated. Ned Stark was against it. Through information from Danerys’ aide, Jorel, Robert Baratheon sent an assassin to poison Danerys. Jorel saved Danerys. Joffrey Baratheon, a protege of the Lannisters, inherited the throne and Danerys’ plot for revenge.
Tyrion is accused of poisoning Joffe, so Danerys will probably turn on Jorel and provide Tyrion with protection.