We are in the central time zone too--- we did the opposite and it worked really well for us. We flew straight to Hawaii (with a 2 hour layover at LAX to walk around- eat dinner etc). Did Aulani and then Maui, and then on the way back we stopped at DLR/CA. Stopping on the way back really helped us deal with the time change. The time change didn't bother us much going to Hawaii. We were so excited to get to Hawaii that we stayed up a full 24 hours from the time we got up at home until we went to bed at Aulani- we were having too much fun once we got there. I was ready to give it up at 23, but DD insisted we were so close we had to stay up the other hour just to say we did. The first morning there we just relaxed at the pool, lazy river, and beach and the time change never really bothered us. Stopping at DLR on the way back, the 3 hour time change wasn't too much to deal with, and then after a few days there, the 2 hour time change once we got home didn't bother us at all.
2 full days will just give you a taste of DLR. Yes, it is smaller than WDW, but there is so much packed into that space. We like to spend 4-5 days there. If you could add at least 1 more day, I would, but if not- I would take whatever you can get. I would also do hoppers-- unlike WDW hopping takes about 5 minutes at DLR-- the park gates are separated by a plaza and are only about the length of a football field apart- it is a shorter walk between parks then it is to walk from the bus stop to the gate in most instances at the WDW parks. . Stopping at DLR on the way there or back would be a great way to get your first visit at DLR in. We used to be WDW people (and to some extent still are). I took DH with me to CA on a business trip and we spent 1 day at DLR-- after that we decided to take ONE family trip there so then pre-school DD could see a show they had at the time- 10 years later and we have been to DLR every year since.