The free dining dates are
2/11/11 - 2/17/11
2/25/11 - 3/3/11
If you want a split stay with both reservations on free dining, you will need to check in on the 11th for the first resort, and the latest you can check out and switch resorts is the 17th, so you would need to do the 17th to the 25th at the second resort. If you do it on the 18th, free dining is not available for the second stay.
Keep in mind that these will have to be separate resort reservations. There is a requirement that you buy at least two-day park tickets for each member of your party for free dining. This means that you have to purchase no less than two-day park tickets for everyone on both reservations.
Disney park tickets get cheaper per day the longer you buy them for, so to split a trip and buy tickets for each separate reservation will cost you much more than it would to just buy the tickets for the full trip with your first stay. Even if you do that, you still have to spring for two-day park tickets on the second reservation if you want continued free dining.
Be careful when figuring out your costs on the split stay. Having to purchase two sets of park tickets might negate most of the savings you may realize from free dining. Even if you are an annual passholder, for this type of reservation you will have to purchase two sets of 2-day park tickets for everyone.
On a 14-night split stay, if you need tickets for the full two weeks, it might be possible for you to book 10 day MYW tickets on the first stay (I am not sure you can buy these for any longer than 10 days) and then 4 day MYW tickets on the second stay.