if it was me and wanted to spend time with the family on the 25th, leave at 11am or so, the 25th is not a heavy long distance travel day. go till about 7-8pm. get up the 26th and hit the road by 3am, kids will sleep the rest of the way in and you will get there around 10-10:30am a head of the traffic.
That is what I would do. I would plan to drive until you got as far south in GA as you could. When we left WDW the 26th last year we didn't leave until around 10 am and we didn't notice the traffic until we hit GA. So you left earlier in the morning from GA on the 26th you should be good!
I've never done a check in around 3am so I have no clue how that works. Maybe try calling the hotels and see how it works.
I know from my house in Cape May county they say it should take 13hrs to get to Brunswick, GA so if you hit the road at 11am depending on exactly where you are you should hit GA by 11pm. Its about 5 hours from Savannah to WDW so even if you get on the road by 6am I think you should be alright. Most people will leave the 26th so you already have a very good head start on them.