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I'm sorry to hear about your situation. The thing about it is that even IF the property would have gone to you if there was a clear line of succession, etc... the fact that the Disney Corporation has resided on the property as though it owns it (or any other resident) then "adverse possession" will apply. That is, even if you have property that was yours, say, 20 years ago (not even considering 150 years ago) and someone else (even a corporation) that purported to own the property for 7 continuous years, legally speaking that becomes their property. That's the formal term for "squatter's rights". You can read more about adverse possession here: http://statelaws.findlaw.com/florida-law/florida-adverse-possession-laws.html
So the court wouldn't go back all the way to 1862, or 1966, or whatever. IF it could be proven that it belonged to you through your heirs, the next question would be whether or not Disney at any point in time possessed the property for 7 continuous years as though it were their own. IF SO, it's theirs under adverse possession. Only if someone else had sole possession of the property for that period of time after Disney acquired it through adverse possession would that subsequent person own it. The point is that adverse possession is a legal transfer of property. So even if they did not get it through a proper transfer, etc... it would still belong to them simply because they possessed the property exclusively and as though they owned it for at least 7 years.
I know this is probably not what you wanted to hear, but it is the law. I hope that clears things up anyway. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable.
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Thank you, ***** ***** luck to you!