For sqlite, when the data to be imported may contain the double-quote character ("), do not use csv mode. The code that reads each CSV field csv_read_one_field looks for it and when it finds it, ensures that it is terminated or expects it to be quoted.
Changing the column separator to ';' won't help because that code will still be executed.
On the other hand, the code that reads each field in ascii mode ascii_read_one_field only uses the column and row separators to determine the field contents.
So, Use ascii mode and set the column and row separators to semi-colon and end of line like this:
*nix:
sqlite> .mode ascii
sqlite> .separator ";" "\n"
sqlite> .import input.csv MyTable
windows:
sqlite> .mode ascii
sqlite> .separator ";" "\r\n"
sqlite> .import input.csv MyTable
However, that will not strip out the double-quotes surrounding your data; they are considered part of your data.