Chicago Family,
Being from Chicago myself and having been there several times over the last 8years, maybe I can offer some suggestions...
for starters, try to part with the Old Style for the 7 days.
Punta Cana is an absolutely beautiful resort area, with emphasis on resort. This area of the country is somewhat bare undeveloped land with the exception of the resorts and the small communities surrounding the resorts. The area is existent for the purposes of the AI resorts. This is not Hawaii, LA, Cancun or the Dells. There isn't allot to do outside the resorts, unless you speak fluent Spanish and are adventurous. You can do excursions at a price, but do not expect a 'Wild Kingdom' level of excitement. Punta Cana is a place to enjoy a beautiful endless beach w/o peddlers every 10 feet, enjoy a the beautiful warm ocean waters and enjoy your surroundings in general.
Personally, if shopping is all your looking for, head down the beach to the flea market stands. Negotiate negotiate negotiate. (Probably a good idea to check things out in the hotel shops to get a perspective on how much things are first, then go to the markets. The hotel shops are obviously overpriced too!)
I've, nor anyone I have traveled with, has gotten sick there. I don't believe the shot is necessary, but I'm not a doctor. Take some Milanta and Tums and don't eat everything you see.
Regarding drinking for the kids, hey... everything is legal unless you get caught! If you look 16 or older, not a problem, although some places tag minors with a special color wristband to indicate underage, so lie about their ages. Regardless, there's no one to police underage drinking anyway.
Sammy who!? Honestly, more locals respond more with the Bulls or Sox.
Things to do... sit your ass on the beach and soak up the beauty. Seriously! Go relax, because that is what I find to be unbeatable about the DR. Don't worry about going here and there. Unless your kids are indoor computer geeks, they should be fine with the beach and pool environment. If you want to go horseback riding, save it for Wisconsin. If you really want an excursion, Safari Outback is my only recommendation. Check out some of the nightly shows. If a disco is your pleasure, go over to the RIU's club (which is better than the average resort "disco". Dance the local dance, bachata and merengue. Probably prepare to get up early at this time of year if you want a beach or poolside chair! Bring one of those cooler drink mugs so you can go fill it with allot of beer while on the beach. Give appreciation when due to the workers and expect them to return the favor by giving you even better service. Tip the bartender and ask for top shelf liquor. If beers your pleasure, the El Presidente will taste just fine for 7 days...
Hope this helps... or at least puts PC into perspective.
GO GO WHITE SOX!!