I have not traveled to Haiti from the DR as a tourist so I have no idea how it works. I have left other countries as a tourist with the intention to return after a short period and in all of those instances, I needed to let immigration know that I was returning, so that I didn't have to pay another fee upon reentry. I usually got a different exit stamp in my passport than someone who was on their way out for good. If you go, please come back and let us know what happens at the border. You should expect to pay some sort of exit tax to the DR (you are after all exiting the country). You will certainly have to pay the exit tax at the airport when you fly home. The $20/$25 cost at the airport may or may not be included in the price of your airline ticket.
Now for the practicalities of a trip such as this. You need to remember where you are. You are not in Sweden any longer. It is not a forgone conclusion that you can undertake this type of a trip risk free. These two countries are rife with institutional corruption. The border region is very much an isolated frontier. You will be a long way from help and the support systems offered by your country's diplomatic mission in the DR. The "criminal element" is omnipresent and this risk is heightened somewhat the further away from "civilization" you go. If you go, at the very least I would inform your embassy here in the DR that you are traveling to Haiti, that you expect to return on such and such a date and you will advise them when you reenter the DR. Not a good idea to put yourself in a situation where you can just disappear off the map and no one knows where you were going or the route you were taking to get there and back.
If you were to park a rental car in the DR and then crossed the border, whose to say your rental car will still be where you parked it when you get back? Since this trip will take more than a day, anything you take with you and leave in the rental car may not be there when you get back to it. Having lots of money with you can allow you to "buy" your way out of a bad situation but can also make you a more likely target for inflated corruption and robbery. Both countries have a well founded reputation for foreigners encountering difficulties of one type or another.
I'm not saying you shouldn't go, if that is what you wish to do. I'm not saying that you will be accosted or become the victim of crime or corruption. I am saying that these things do happen from time to time and the probability of something like this transpiring is much greater on this side trip than travelling between say Sweden and Norway for a day or two. This trip by its very nature, involves an elevated level of risk to your person and property. Malaria is endemic in the border region as is cholera. Just by going you will exposing yourself to circumstances that you may not be anticipating. I can't tell you to go or not to go. That's up to you. Potentially, a trip of this nature, in this political climate, between these two countries at this time, is not an easy and necessarily straight forward adventure. It can turn into a really big fiasco on either side of the border without a whole lot of forewarning. "Your eyes need to be wide open."
Good luck whatever you decide.
