FrogReaver
The most respectful and polite poster ever
Also, in rules jargon, there is no need that an improvised weapon be considered a weapon (unless your dm rules the improvised weapon to be so close to an actual weapon that you can use the actual weapons statistics).
So my ruling would be that a shield is an improvised weapon but not similar to any actual weapon and since two-weapon fighting requires you to wield a weapon and the dual wielder feat only lets you ignore the light part of the two-weapon fighting rule then I rule against being able to two-weapon fight with any improvised weapon that doesn't resemble an actual weapon well enough to use it's statistics in place of the normal improvised weapon damage.
So my ruling would be that a shield is an improvised weapon but not similar to any actual weapon and since two-weapon fighting requires you to wield a weapon and the dual wielder feat only lets you ignore the light part of the two-weapon fighting rule then I rule against being able to two-weapon fight with any improvised weapon that doesn't resemble an actual weapon well enough to use it's statistics in place of the normal improvised weapon damage.