How to mix small amount of alcohol into coconut oil
When you consider that rum and most other hard liquors contain at least 50% water, it is not surprising that the result is a two-phase system. If you began with absolute or 95% ethanol, or perhaps even grain neutral spirits, which vary but often come as 180 proof (90% ethanol) you might get the homogeneous solution you want. Another approach would be to add an edible emulsifier such as lecithin, which will help the ingredients to form a stable emulsion.

The earlier suggestion to hydrogenate the oil is not likely to work, as hydrogenation does not make oil able to mix with water. Coconut oil already has a high saturated fat content, as can be seen by the fact that it is often a solid at room temperature.