Yes, there is slang, just as there is in the US. For example, you have words in Maine that aren't used in North Carolina. But don't worry about it. Just continue what you are doing to get the basics. You can't get the rest without a lot of experience using the language. And even then, if you are like me, you will never be able to stop learning.
Your children, on the other hand, are likely to surprise you with the speed they pick up the language once they are playing with Dominican children. They will soon be way ahead of you in their ability to converse in Spanish.
With respect to slang, you hear much less of it when you are conversing with people with a good education. They are also much easier to understand since they speak slower, more distinctly, and are less inclined to run their words together.
The important thing when you are here is to speak Spanish at every opportunity. Don't hold back just because you aren't able to express yourself as well as you can in English. You only learn through much use and making frequent errors. Your best friends will be those Dominicans who correct your errors; this is something you should encourage them to do. You are much less likely to repeat a mistake if you know you have made it.
Remember your children when they learned English. You have to go through the same process in learning Spanish, even though you are an adult.
PS: I have always appreciated the advice of the person who told me to always speak good Spanish, not the Spanish used on the street. A small example: I always say buenos d?as even though most on the street say buen d?a. (Educated Dominicans more likely to say buenos d?as.)