While your ideas pose interesting questions, you are assuming too much and asking further questions based on wrong assumptions.
The reduction of the polar ice fields will only have a very minute affect on sea level, a very small rise. (The rise of sea level is caused by the expansion of water as its temperature rises and other factors involving plate tectonics and isostasy.) However, the larger volume of water does not directly influence the size of tides. (Also tides have little to no affect on weather systems.)
Tides are mainly a result of the orbit of the moon around the Earth (the Sun also plays it's part - spring and neap tides) The gravitational attraction of the moon causes the seas to bulge out in the direction of the moon. Another bulge occurs on the opposite side, since the Earth is also being pulled toward the moon. The size of the tide is dependent on the size of the gravitational forces working which are relative to the distances between the Earth, moon and Sun.
To see a more dramatic tidal shift, as you describe you would have to move the moon closer to the Earth, as Jim Carrey does in Bruce Almighty, but in reality this is impossible. However, if this happened, the greater friction (water resisting movement) produced would slow the Earth's rotation more quickly than at present. Since its formation the Earth's rate of rotation has been slowing due to all forms of friction acting on it including tides.