He couldn't have killed her with a single thought because of her extensive mental shields. Well, he probably could have, but it would have taken some time. When Rhys tells Feyre what happened when Amarantha took over, he says that he was too busy trying to break through her mental shields to notice the spelled (or poisoned, not sure which) drink. Which must mean that even for him, her shields were very strong, and would have taken more time and effort than they had at the time when Feyre broke the curse.
Now onto why it was Tamlin that killed her. I think it was because Rhys tried before the curse was actually broken (so he wasn't at full strength), and failed. Then, once the curse was broken, he wasn't strong enough to be able to do it himself.
Now onto why he was planning for Tamlin to do it. Now this is probably the least thought out of my three paragraphs, but I think it was because he wanted to maintain his image as a "bad guy". If he was the one to kill Amarantha, people would probably wonder why he suddenly had a change of heart. And at this time he was still trying to keep Velaris a secret. So, he planned ahead and made sure someone else, who everyone expected (a.k.a Tamlin), killed her. Then he made Tamlin angry to give him the best possible chance of killing her, even if things went a little south.