I was just at the Holiday Inn Sunspree from June 3-10 with my wife and 2 year-old daughter. The Holiday Inn itself has a number of activities for kids, including contests (e.g. ice cream contest, coke drinking contest), Family Bingo, arts and crafts (e.g. kids get to make a note pad, decorate a lizard etc.) and day trips off the resort (e.g. the hotel takes families to the Butterfly farm during the week ($10 for adults/$7 for children). At night there is usually a show that begins at around 8:00 - 9:00 PM (limbo, carnival etc) and there are also movie nights by the pool (they had Spiderman 3 and Fantastic Four while I was at the resort). I would highly recommend the resort for families with kids.
Some additional tips:
It is very safe to walk around Aruba, especially in the hotel zone around Palm Beach. If you go to the Radisson hotel (just down the street from the Holiday Inn by the Butterfly Farm) around 11:00 AM in the morning, the bird keeper will be cleaning the bird cages. He will allow you to hold and take great pictures of the exotic birds for no charge (e.g. parrots in your hand/on your shoulder). Across the street from the Holiday Inn, there is a booth that charges tourists for the same picture.
The hotel allows you to use snorkelling gear for free. I borrowed some from the hotel and brought it to Baby Beach on a day trip and was able to enjoy some fabulous snorkelling. Rafts can also be rented by the beach at a cost of $5 per day (you may want to bring your own inflatable raft to the resort).
I would recommend that you rent a car (a 4X4 if you plan to go to the other side of the island) and go with your family to see Aruba's sites. There are a number of reputable companies with booths that rent cars inside the Holiday Inn and this is probably a cheapest way to see the island (paying for a guided tour of the island for the four of you would be much more expensive).
If you are planning on going to the beach and want some shade, you will have to get up to reserve a hut (the Holiday Inn has about 100 on the beach). I was able to get a hut around 8:00 in the morning when I went to reserve one (although keep in mind that there were few left at this time and I went during the low season). Many people get up at 6:00 AM to reserve huts (and wait an hour for the booth to open up to do so) and are not in the mood to share their huts. The huts by the pool cannot be reserved and are available on a first-come-first-served-basis (the zero entry pool at the Holiday Inn is especially great for the younger kids).
While the buffet at the Holiday Inn is adequate (very good for breakfast), the Sea Breeze and Davinci restaurants offer better meals for dinner (keep in mind that Davinci's has a dress code when you are packing). The hotel takes reservations for these restaurants at 8:00 AM each morning (one restaurant was open/one was closed each day on an alternating basis while I was at the hotel). The prime times for eating at the restaurants (i.e. between 7:00 PM and 8:30 PM) book up very quickly, hence, I would suggest that you line up to reserve a time if this is when you like to eat. I should also point out that there were other kids in the restaurants while I was at the Holiday Inn (i.e. you do not have to worry about whether your kids are allowed to eat in the restaurants) and the Iguana bar by the beach/pool is very convenient to grab a quick bite of food during the day with your children (they serve food at the bar until late in the evening).
Jolly Pirates is located right next to the Holiday Inn on the beach. They offer a very reasonable snorkel (daily)/sunset cruise package (on Mondays and Fridays) that is great for families (check for a $10 off coupon in one of the books that they give you at the airport).
If you are not on the Holiday Inn's all-inclusive package, I would suggest that you go off the resort to eat and buy your beer/liquor/snacks at the local supermarket. Indeed, there are a number of restaurants nearby that are a little better value than the Holiday Inn e.g. dinner for myself, my wife and daughter would normally cost around $100 on the resort and drinks by the pool/on the resort are expensive ($2.50 for a coke/$4.50 for a draft beer/$5.50 mixed drink - the drinks are the size of a small dixie cup). I found the all-inclusive option to be a great value and heard a lot of complaints about the resort prices from those that were not on the all-inclusive plan.
There is not much in town for kids (mainly jewelry/souvenir shops). However, souvenirs are a little cheaper in town than on the resort if you/your kids must have that giant stuffed iguana. Local vendors also set up booths around the Holiday Inn's pool at night a few days during the week if you are looking for souvenirs.
The Aruba and Bonnaire towers have been renovated at the Holiday Inn while the Curacao tower has not been renovated (it will be renovated later this fall). Hence, I would suggest that you request one of the renovated towers before you go down (perhaps send the Holiday Inn an e-mail a week before you arrive - my personal preference would be in the Bonnaire tower overlooking the pool). While the newly renovated towers do not have bath tubs (only showers) they are further away from a local beach bar (Momba's), which can be loud on some nights (not the best for kids).
My wife an I also brought our GMRS radios to the resort. The radios worked great in Aruba and were very helpful around the resort, especially when discussing reservation times for dinner/which huts to book by the beach. The radios also allowed us to keep in contact with one another when one of us would go to the casino at night (children are not allowed in any of the Aruba casinos).
Bring lots of suntan lotion. It does not feel very hot in Aruba (i.e. with the trade winds constantly blowing), but you burn quickly given the proximity of Aruba to the equator. Sun tan lotion is also very expensive to buy in the hotel if you run out of it.
I hope that helps. Feel free to ask me any other questions about the resort.