Kids are 11, 9, 7 and 4. The older two were at Disney as babies, otherwise this is a first and first December for kids. We don't plan on going back to Disney prolly for another 10 years! The day we thought about going is our arrival day, Tuesday the 11th. We arrival at Mco at 11 that morning, so we could rest until 4. Just not sure, bc I hear so many conflicting reports about it being very crowded.
Considering all of that, I would say go for it!!! I would just definitely have a stroller for the youngest, or maybe even a double for the youngest 2 so even if they fall asleep, the rest of you can still enjoy everything!!!
If there is a must see character, do that before the kids fall asleep, and don't waste a lot of time on doing a "table service dinner" during the party hours.
Tuesdays generally aren't as crowded as weekend nights (Orlando locals) and I am pretty sure that the week you are going is still just a medium crowd level, so you may luck out with that.
Since you won't be getting to your resort until after 12-12:30, I would grab some lunch, visit the arcade or maybe even the "quiet pool" if it is warm enough, just something that won't be too exhausting, but keep the kids from going MAD with excitement.
Which resort are you staying at? And are you planning on using Disney Transportation? The reason I ask, is because, if you are planning on taking the bus, you will want to head out around 3, by the time you get to the bus stop,wait for the bus, get to the park, walk to the gates etc.etc. it will take you almost an hour. (that's IF you want to be there @ 4)
I say go for it, you will probably get more out of it (as far as your older kids and your plan) than I did. (but like I said, our mistake was being in MK
ALLLLLL DAAAY LOOOONNNGGG)