As many of us are already aware, the amount of creams, gels or other type of liquids we carry on board when we fly has been restricted since 2006, down to one clear plastic bag (available at the airport) containing 3 ounce bottles of liquids. Check with your airline regarding other hand luggage items, such as baby food or medication.
Many items can be restricted for carrying in hand luggage, even seemingly harmless ones, like umbrellas. It's best to do thorough research, and if in doubt, put something in your checked baggage instead of carrying it with you on the plane. Likewise, you cannot take “long cord” appliances onto airplanes. Likewise, there are restrictions on checked baggage as well - again, you should check with your specific airline about this.
While it may seem unusual, bringing batteries into the Dominican Republic is regulated; don't take too many with you (unless you want to risk them being taken by security), and become familiar with the guidelines surrounding batteries before you go
Before traveling to the Dominican Republic, you should read the website of your airline just to find out what items are allowed in checked baggage and which are not, because each airline has its own specific rules.
Overweight luggage can incur costly penalties; weigh your luggage before you leave as a matter of habit, and check with your airline about weight limits. Always pack light and leave room to bring back things with you if you wish to.