Had a similar thing happen to a company I was involved with a long while ago. (The VC involved was far from the valley.)
In fact, the partner even resigned from our board during acquisition negotiations, because the squeeze he was attempting, enriching his firm at the expense of other shareholders, wouldn't mesh well with the fiduciary responsibilities of a board member.
Some people think using every lever at their disposal to eke out a few extra percent at the last minute proves their business mettle. I suppose they expect – or prefer to guarantee – that this be their last transaction with the others affected.
We wound up acquiescing to his demands to avoid ruining the acquisition. And most of us resolved to never do business with him or his firm again.
If another acquisition materializes, you may just have to acquiesce and/or play chicken/hardball with this VC – all the while hiding any internal dissent from the acquirer, so that ultimately it's up to you and your investors whether you walk away from a deal.
If he's a bit player at a larger VC firm, you might privately share your concerns with other more senior partners there – which almost always would be a relationship-destroying maneuver, but if the relationship is already kaput, why not?
Hardball might involve having your own lawyer find the maximum you can do under the investment agreement without the VC's agreement – asset sales, de facto liquidation, etc. – or find grounds to (credibly threaten to) sue the VC for breaches of various duties.