What could the legislative branch have done more constructively regarding Reconstruction and civil rights between 1865-77?
Congress was fairly successful at politically reconstructing the country, as they found a legal and simple method to readmit the southern sates to the Union, and amended the Constitution to end slavery and legally define the freed slave population. But this is about where their success ended.
The Freedmen's Bureau, set up to offer education and training to former slaves, was woefully underfunded and neglected, and after only 6 years of operation its funding was cut. Another ten years of such a program would have worked wonders in terms of economic and social equality for blacks in the long term.
In addition, if the "40 Acres and a Mule" plan of redistributing land from the plantations into the hands of freed slaves had actually taken place, civil rights equality for blacks would have come much sooner, in my opinion, as it would have followed their economic equality, which also would have come much sooner. As it was, sharecropping replaced slavery and held the freedmen in the same social and economic bondage as before the war.
Lastly, with a large Union Army presence in the South during those tweve years, they could have more aggressively pursued violent organizations like the Ku Klux Klan, and taken the protection of former slaves more seriously. To do this, the President and the Congress could have placed abolitionist commanders in charge of the occupation army.