Interpreting high precision and very low recall score
All problems due to "a very imbalanced dataset". Please look at the definition of recall and precision. Based on your score I could say that you a very small set of values labeled as positive, which are classified correctly($precision=\frac{TP}{TP+FP}$). But you have a very big set of values labeled as negative, which have influence on $recall=\frac{TP}{TP+FN}$, in that way that $TP$ stays the same like in precision, but have you a lot of $FN$ values which leads to small value of recall.

At least you should resample of the dataset to make better results.