Ok,pals, I solved it 
I'll not be greed and I'll post what was the problem, maybe someone else needs it...
-Problem was that I was saving the date in the SQlite database, but when I went to use those dates for comparisons, conditions returned always 'false', and from command line, sqlite operation "date(mydate)" returned an empty string (while it should return the formatted string).
Solution: the problem persists probably because we saved the date string in the wrong format. In order to let the database understand the date and operate with it, the string must be in the format "yyyy-MM-dd", so with QDate it would become:
query.bindValue(":mydate",ui.dateEdit->date().toString("yyyy-MM-dd"));
query.bindValue(":mydate",ui.dateEdit->date().toString("yyyy-MM-dd"));
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finally to get a result using BETWEEN is just needed the following:
SELECT * FROM mydatetable WHERE mydate BETWEEN '2008-07-22' AND '2008-07-25';
SELECT * FROM mydatetable WHERE mydate BETWEEN '2008-07-22' AND '2008-07-25';
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Here we go.
(It would be nice if someone spends two words remembering it on sqlite docs... at least I should have economized two hours, and someone else in my situation...)
Hope this can help
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