I've been looking into this for awhile now. I have a level 4 Dragonborn Paladin with the Dual Wielder Feat. I currently have two warhammers, but I'd like to use two mauls for the extra dice. After all, 4d6 is better than 2d8. If this isn't something that would work, that's fine, but it'd really be nice.
No, you can't use a two-handed weapon with one hand.
Two-Handed. This weapon requires two hands when you attack with it.
Even if you could, two-weapon fighting is defined as
When you take the Attack action and attack with a light melee weapon that you’re holding in one hand, you can use a bonus action to attack with a different light melee weapon that you’re holding in the other hand.
And the Dual Wielder feat says that you can
use Two-Weapon Fighting, even when the one handed melee weapons you are using aren't light.
So even if you were somehow (maybe magically) capable of wielding two-handed weapons in one hand, you still wouldn't be able to use Two-Weapon Fighting with them, because even with the Dual Wielder feat you are still required to use one-handed weapons.
From the equipment list in the PHB on page 149, a Maul is a two-handed weapon. The rule for two-handed weapons is on PHB 147:
Two-handed. This weapon requires two hands to use.
Since you must use both of your hands in order to wield the maul, you wouldn't be able to wield a second weapon.
You can wield the warhammers because they are versatile, and you just opt to always use the one-handed damage while dual-wielding them.
There's nothing directly in the rules that would let you. However, D&D rules are bendable. I had a barbarian player who wanted to dual wield great-swords mostly for the aesthetic. Frankly I liked the idea but I didn't want him to be OP, so we worked out a compromise, he had to attain a strength above 20 and the damage die would reduce to d10s when dual wielding. This made it fair and it also made him feel badass. Point is this is a fantasy game and rules can sometimes be ignored as long as the result doesn't break the game. Work with your DM and find a compromise.