The role of an ambassador is an important one and should be carefully picked based on how well they represent your country and how well they get along with the host nation.

The role isn't solely chosen by the guest nation. The host nation has a say in if they want or do not want them.

So Domenican Republic gets to accept or reject the ambassador. The reciprical response would then for the US to do the same to the current Domenican Ambassador. If they were really upset they also pull back some aid programs as a wrist slap.