Some useful commands I'd use in scenarios like this are:

  git add -p # select what to add to the staging area
  git reset -p # deselect chunks that I decided I don't want anymore
  git stash # saves your working state in a temporary commit (not in your branch)
  git stash pop # restores the working state from the last git stash command and drops the temporary commit
  git rebase -i $start_point # where $start_point is either a branch or some commit in your branch history. -i means interactive, which allows you to reorder/edit/reword/squash commits
  git checkout -b $newbranch $start_point # you can make a new branch at any commit in history, so if you decide to reorder your commits, then declare and older commit as a branch and get it merged first, that's fine. $start_point is optional, if unspecified the current HEAD commit is used.

For your specific example, with a staged partial commit on branch idea-1, I would:

  git commit -m 'WIP idea 1'
  git checkout -b idea-2 HEAD~1 # makes a new branch at the parent of the HEAD commit
  git add -p # pull in the desired changes
  git commit -m 'idea2 implementation'
  git checkout idea-1
  git add -p # stage the rest of the changes
  git commit --amend
  git rebase idea2 # if idea 1 depends on idea 2

I do wish git had some notion of sub-commits with their own messages, and a better UX for cleaning up a set of commits before merging them.