We had a couple places where police would stop us and ask for our passports. I would suggest not giving them your passports - this is where a driver can come in handy as they will handle all of that and take care of you.

Besides that, it’s generally pretty safe in the tourist areas because they have police specifically for tourists, but when you are out and about it other areas, just be a little more aware of your surroundings.

If you need a good tour guide for a fun boat trip out to visit an island called “isla Saona”, BM me and I can send you it. It’s an all day trip where you can go snorkel and then basically have a private beach for as long as you’d like. And the guide I can introduce you to is awesome and speaks English as well.
(I did an internship there a couple of years ago.)