As a graduate student in algebraic topology, but one who has taken many "second year" graduate courses in algebra, the one I think I would have enjoyed the most had it ever been offered (and the one which would have been most useful for me personally) would go something like this:
Textbook: An Introduction to Homological Algebra - Charles A. Weibel
What to cover:
- Chain complexes and homology
- Derived functors, Ext, and Tor
- Spectral Sequences and/or homological dimension depending on which direction you want to go
- Group Homology and Cohomology (I really enjoy Weibel's treatment of this)
- Lie Algebra Homology and Cohomology (here you can bring in lots of related topics)
- Last chapter and appendices on category theory and the derived category
I agree with Richard Rast a bit that no one course can cover all the topics you like, but I think Weibel does a great job setting up the homology/cohomology framework using category theory and lots of homological algebra, applying this machinery to group cohomology and representation theory, and also bringing in classical groups. This seems to cover most of what you mention in your question.
A supplement I used when following this model on my own was Representations and Cohomology Parts I and II by D.J. Benson
