I wouldn't bother making a reservation for a shuttle from the airport. After you get your bags, walk out the doors and look for the sign for "shuttles and taxis" (something like that, I don't remember the exact wording).
SuperShuttle is the "blue" shuttle. There should be someone standing at the curb in a blue SuperShuttle shirt holding a clipboard and a walkie-talkie. Tell the person you need to go to Anaheim and the person will get on the radio and call for an Anaheim shuttle to your stop.
Within five minutes, a shuttle should pull up with a sign that says "Orange County/Anaheim" or "Anaheim/
Disneyland" - something like that. Tell the driver what hotel you need, give him your bags and get in the van. You may have to make a couple more stops to fill up the van before you leave, but it shouldn't be long before you're on the road. I think each shuttle holds 10 passengers, so your 4 will help fill it up.
Airport Bus is probably the company you went with last time. They're a little cheaper, but they only run a bus every hour on the hour, so if you just miss it, you're going to be waiting, and unless your hotel is right beside their depot (by the Howard Johnson's across from Disneyland, I believe), you have to transfer to a smaller shuttle that'll take you to your hotel. SuperShuttle drops you right at the hotel.
There are other shuttle companies around, but I think they're all the same price, and I haven't really heard any bad things about SuperShuttle.
The last time I was in Anaheim, I had the hotel make my reservation for the shuttle to the airport when I was leaving, and they called some other company that never showed up to pick me up. The hotel called SuperShuttle, who sent one of their drivers to get me and I got to the airport with plenty of time to spare, despite leaving almost an hour later than I should have. For that reason alone, I wouldn't hesitate to use SuperShuttle again.
That was two years ago, so their prices have probably increased a bit, but I believe it was $14 per person each way for SuperShuttle (I don't know what their kids' prices are). I think Airport Bus was $12 each way, so it is a little cheaper, but you risk having a long wait - as you've already discovered.