We didn't have any vanilla infused white rum, but used a drop of vanilla extract (not essence, cannot abide the synthetic flavour/smell, it reminds me of sugar chemistry in the lab when I was doing my chemistry degree, benzaldehyde is used as a protecting agent !). This was one of our more favourite grapefruit containing cocktails.
I used the Rum I had which was - Plantation 3 Stars rum (not vanilla infused)