Where did you get the idea that the board minutes had to be approved unanimously? The action to approve minutes is the same as the action to approve any other item on the agenda that does not require a super-majority. Normally a board acts by the vote of a majority of directors present at a meeting at which a quorum is present. It is okay to have negative votes, but they don’t control the outcome if a majority votes otherwise.

If the new director wants to vote No, you should ask her to explain why. If her explanation is that she didn’t agree with the decision, that is irrelevant to the question of whether the minutes are accurate in recording the vote that was actually taken. If you record the reason for her objection, a later reviewer will realize it is irrelevant. 

One could argue that it is a breach of fiduciary duty, and not an action taken in good faith, to vote against approving minutes that she realizes are accurate but that she would like to show a different outcome.  Instead of voting No, she could always abstain.  In either case, if a majority approves the minutes, you can record that vote and move on.  She has no power to hold the board hostage unless you let her.