We went this past year over NYE and we had a great time. However, you need to be prepared for very large crowds. I have been over spring breaks before and they didn't compare to NYE. You'll definitely need to stay for at least a week if you plan to all the rides, which with small children it would be hard to tell them they are just in Disney to absorb the atmosphere so I imagine you'd be focusing on rides and holiday events. We stayed 12/27-1/4 and were able to see everything we wanted to. This, however, did not include visiting many characters for photos, autographs, etc. If we passed a character with no line or a very short line we would go, but other than that we skipped most of them. Additionally, we stayed onsite. Though it may be cheaper to stay offsite during this time of year since the prices onsite are so high, it is almost a necessity to stay onsite due to the crowds. Definitely look into the All Star rates for when you'll be there as you may be able to get a cheap rate. If you arrive before a certain date you can get the value rates and also those same rates go back into effect 1/1 so make 2 reservations if you have to. While we were there, AK filled to capacity once and so did MK and as a result if you had gone in the morning, left to nap or rest during the day, you may not have gotten back in when you returned. We never napped during the day on previous trips, but the crowds really exhaust you so it was necessary for us. Also, the lines midday are about 1.5-2 hours, even at less popular rides so if you want to see anything at those times prepare to wait in line a very long time. Fastpasses also didn't help much midday as the return times were usually late evening (we got one for Test Track at 1pm for a return time of 7:30pm on 1/1, around 2:45 all the fastpasses for the day were gone and the ride had shut down due to mechanical repairs; when it went back up the standby wait was over 2 hours since there were no fastpasses left). Because of this, we found it much more practical to wake up early and arrive at the designated EE park for EE (which was 7am for most parks until 1/1). We would then stay at the park until about 1-2pm, then go back to the hotel and nap or just relax, and then go back around 6pm when the crowds were thinning again. Doing it this way allowed us to get on every ride and see every attraction, with the exception of most of Mickey's Toontown Fair and the parades since we had seen them all last December. Without EE, however, we never would have been able to see this much as the extra hour was a huge help, also, the offiste guests formed long lines to get in at regular opening times that if you were not in the front of the line you'd have to wait about 15 minutes to get in.
As far as NYE parties for young kids, there aren't really any geared towards them, as the majority of events are at Pleasure Island, the Boardwalk, and restaurants such as the California Grill. Kids are welcome at many of those parties, though the price at California Grill for example was $300/child and $500/adult. However, the general festivities at the parks are included in your admission price and are a great way to celebrate. You'll get hats, horns, fireworks, etc. So with the kids, I would opt for that, however just be sure you bring some ponchos along as this year it rained all night long, and pretty heavy too.
No matter where you stay or what you do, you'll have a great time as it is a very festive place to be for the holidays. Just be sure to keep EE in mind when you decide on where to stay and also that if you plan to leave and come back later in the day, there's a good chance you won't get in if you're offsite.
IT's cheaper with my DVC points!
