There is only so much you can stick in a carry on for 4 people, especially when you have a 2 and 3 year old! All my other carry on's will be holding DVD players, DVD's, toys, etc for the plane ride.
Do what you feel is best for you.
However, if I were traveling with a 2-year-old and a 3-year-old who cannot carry their own bags, I would welcome the opportunity to have Disney retrieve the checked bags behind the scenes at the airport and deliver them to our room, without charge (not even tips). And I would welcome the opportunity to be on a motorcoach to WDW as quickly as possible, rather than spending an extra 30-60 minutes at the airport dealing with luggage (and the kids) before departing.
To me, it seems that a change of clothes and a swimsuit for two toddlers would not take up much space in carry-ons, even if those carry-ons also have some toys in them. (By the way, you should always pack your carry-ons with essential items that you'll need if the airline delays your bags, which is quite common).
We arrive at 9:30 AM at the AP, so maybe it won't be the crowded on the bus???? Anyone know if the mornings are less busy on DME?
DME schedules to appropriate levels based on the expected number of guests.
With a 9:30 a.m. arrival at the airport, chances are that when you arrive at the resort, your room will not yet be ready. You'll have check your bags with bell services. Then, after your room is ready, you'll have to retrieve your bags in the lobby or have a bellman deliver them to your room. In either case, it's appropriate to tip, so you might as well have the bags delivered to your room. You will need to wait in your room if bell services is backed up because you need to be there to tip the bellman. And, under these circumstances, you'll have your bags about the same time that you would have received them through the free DME luggage transfer service.
Again, please do what you feel is best for you. I think you've made up your mind.
The reason I'm posting this reply is to help others see that throwing away DME's inbound luggage transfer service leads to more time at the airport, having to deal with bags at the airport and hotel (especially if you have young kids), tips to the DME driver and bell services, and, overall, a more aggravating way to start a WDW vacation.