How to optimising caret for sensitivity
Probably.  It depends on what you are doing exactly, and in particular which summaryFunction you are using.  If it's twoClassSummary for common binary classification then you should be able to specify metric='Sensitivity'.  If that's not the case you also have the option of overriding the default performance summaryFunction with your own implementation that calculates the metrics you desire.

I highly recommend reading through the documentation at http://topepo.github.io/caret/training.html#control