Associate editor's dilemma with inconsistent first/second round review
The reviewers make recommendations to you, not judgements.  As the associate editor, you have to decide how to interpret those recommendations, taking your own judgement into account.

I think that it is actually reasonable for a reviewer to become peeved if issues that they think are important were not addressed, and therefore judge a paper more harshly.  Usually that goes Major->Reject, rather than Minor->Major, but if it was borderline for the reviewer before, it's not bizarre. The real question is: do you agree that those issues are important?

If you disagree with the reviewer, you can recommend minor revision or acceptance.
If you agree with the reviewer, however, that this paper has some real issues that need to be addressed before it get published, then it's entirely reasonable to request another revision, even a major revision.  In your editorial statement, you then say something like:


  In particular, Reviewer #1 points out that the following issues in the original manuscript have not been addressed in the revision, and these must be addressed for this paper to proceed toward publication: [key issues]


Now the authors have a clear editorial directive for what exactly must be done in their revision.  If they follow this directive, all well and good and they get published; if they refuse to follow it, then you have reasonable grounds for rejection.