Hi Ralph, I think the name is Dance Son.
The steps seem to be similar to the ball room dance. the actual music Son or at least the steps seem to be different in both pattern and rhythm. I don't think that there is such a dance called rumba son. there is a style of mixing guaguanco and son together, but the actual dance is more of a couple's thing.
The rumba term is for sure a gathering of musicians dancers and singers to have a great festive time, I do know that. I didn't realize that other islands in the Caribean used the Spanish word to describe what they do also.
I remember something about the word rumba beingfrom the word rumbo something to do with a boat, but I forget exactly.
Anyway I was just curious how the dance you do
came to be. I didn't realize that it hadn't anything to do with dances of guaguanco, yambu or columbia or rumbas del tiempo de espana which are the main rhythms used in cuban rumba.
Thank you Ralph, now I understand a little better.
Clifford

A couple of other variations.

1. After the UAT the lady steps to the side (closing to the man) with her left foot on slow then into a second position break for QQ. The man does the oposite.

2. One of my favorites is for the man to lead lady to do a 5th position break while he does a 2nd position break. Because they are moving in different directions, it creates a "slingshot effect" with the couple coming together, then apart (to show off the lady) and then back together again in a basic box step.

Here are a couple of ways:

1. After the lady turns on QQ and steps to the side on slow, standing on her left foot, she'll bring her right foot to her left and change weight, then change back to the left. Man, of course, does the same only on the other foot. Also known as a side basic...now they both have the correct foot free to step into a box on slow.

2. When lady steps to her left foot on slow, do a fifth position break and straight into the box (lady turns to her right and steps back on her right foot, then replaces to her left swiveling to the left to end up in front of the man, right foot stepping back. Man steps back into the fifth position on his left foot, then replaces weight to his right foot bringing the lady in front of him, then forward on his left foot into the box).

(2) is a particular favorite of mine! The separation when the man and woman are doing their 2nd and 5th (respectively) has a very nice look.