Yes, Obama should object to David Miranda's U.K. detention, because his detention was nothing more than retaliation for his connection to Snowden. Miranda did not do anything wrong himself. The United Kingdom decided that he was guilty by association and that they were going to make an example out of him.
Obama as the head of the western world has to obtain and keep the allies in case of a war of international upheaval. Detaining David Miranda would separate the United Kingdom as a needed ally in war. Keeping allies is crucial especially in the wake of the uprising of terrorism.