To begin with: If you're having a Dominican family over for dinner just be yourself as they will expect to mold their visit around your "style", this said Dominicans enjoy every single part of their daily lives, eating and drinking it's just as fun as going to the beach, we love to engage in a wide range of issues when at the table since it's one of those moments when families do come together at home, don't expect them to be waited on or need to have a salad fork etc laid out on the table for an "Alta Etiqueta" dinner, the normal 3 piece of flatware should do just fine, my family loved to serve a chilled wine with a good dinner I don't see how this could hurt, some Lancers or Martini & Rosse could just do the trick, kids are mostly allowed to behave with the same freedom an adult has while at the table, by this I mean not to expect them to be eating everything served on your menu if they dislike it or plain and simple looks too unfamiliar to their eyes yet good conduct it's the rule of the land and you're expected to impart some of it with freedom, unlike other cultures Dominicans see other people's calling their child to good conduct as a need for their social integration and most of the time a must, just act as if you were having over your sister's kids for brunch and all will fall into place soon thereafter.
But of course a sweet dessert it's all but expected after a extraordinary dinner, a black cafe wouldn't hurt a bit and some sweets for the children would help bring about an ear to ear smile on the children at best.
Right after dinner it's when the action takes place, lively conversation would be floating around the room soon thereafter, children are expected to go play around in some other room within an eye shot from the adults allowing for an adult's only lively discussion on many topics of which many family related stories would be the prime rib, load your pockets with some of your family "funny moments" and you shall reign victory over the clan!
Don't expect them to come black tied and nightdress attired, for the most part when we visit good friends Dominicans are casual in their dressing, the more casual the more they feel at home with you.
If you want to captivate the children attention depending on their ages of course, you can have some rental movies handy by the DVD or VCR to ease the moving around of the children in the house.
And last but not least: Have fun! you're expected to engage with them in having a good time.