It is not so much the weight of the engines, but the dimensions.
Depending on what a/c it is (757/767/A330), will depend on how big the door on the transporter needs to be.
Some engines, when they are less urgent AOG parts, travel on 747 SCDs or nose loaders on schedule cargo services, but I doubt the Dominican Republic is served frequently by such aircraft.
So, instead of having to pay £10,000s a night on pax hotels/food etc, and losing money on missed schedules in the following days and weeks, it is often more economically sound to use a dedicated charter a/c.
Certainly not a cheap option for an airline though - several hundred thousand dollars at least.