Hi Ken and welcome to the board
Quite a story you have there. I've just Googled Piriapolis and it seems it's close to Maldonado which was my first real taste of civilization after leaving Antarctica after 2 years. Our ship docked at Montevideo and then a friend and I took ourselves on up the coast on a slow journey to La Paz where I flew back to the UK from. I really liked Uruguay, a nice place off the beaten tourist track with very friendly people.
The Argentinians have had families on the Peninsula for many years now and at one time even used to fly women down to give birth to genuine "Antarcticans" to help boost their political claims. So families aren't that unusual.
The US has had a programme whereby teachers and sometimes (older) kids can visit for some time now. As far as I'm aware there have been no families there (other than on tourist vessels), there is no particular reason to do it, and most people who go to Antarctica go for a reason to do with what they can do (research or research support wise) in Antarctica. Having said that I have always been a believer in don't-ask-don't-get, so good luck.