J Lo and A-Rod packed on the PDA Tuesday in the Dominican Republic, where they've been working through some serious relationship issues. They certainly look like a couple, kissing and conversing on a balcony. But, there's no doubt ... they know cameras are trained on them.

The sparks were flying, and not just between J Lo and A-Rod ... they were even treated to a fireworks show, which Jen seemed to love, throwing her fists in the air.

Cameras or not, it seems like a good sign for J-Rod ... and their 4 kids. As we first told you, the children are a big reason why J Lo and A-Rod are giving it the ol' college try in the DR ... trying to patch things up.

Seems Alex made the right move in visiting Jen in the Dominican, where she's been shooting a movie. He fueled up the jet Sunday and flew down from Miami. A-Rod was feeling good about their prospects Monday, saying things were onward and upward, and the next day they were smooching.

TMZ broke the story ... people close to the couple acknowledged things between J Lo and A-Rod blew up Friday, TMZ and other outlets reported the couple broke up Friday -- sources directly connected to the couple told us so. We're told someone said "It's over!" in the heat of the moment, but by Saturday morning J-Rod was telling us "We are working through some things" and their issues had nothing to do with a third party.